UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
                                  ------------

                                  SCHEDULE 13D

                    Under the Securities Exchange Act of 1934


                              Triton Energy Limited
                                (Name of Issuer)


                           Ordinary Shares, Par Value
                                 $0.01 Per Share
                         (Title of Class of Securities)

                                    G90751101
                                 (CUSIP Numbers)

J. Barclay Collins II, Esq.                          with copies to:
Executive Vice President and                         Timothy B. Goodell, Esq.
General Counsel                                      Gregory Pryor, Esq.
Amerada Hess Corporation                             White & Case LLP
1185 Avenue of the Americas                          1155 Avenue of the Americas
New York, NY  10036                                  New York, NY 10036
(212) 997-8500                                       (212) 819-8200


            (Name, Address and Telephone Number of Person Authorized
                     to Receive Notices and Communications)

                                  July 9, 2001
             (Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(b)(3) or (4), check the following box |_|.









CUSIP No. G90751101 (Ordinary Shares)       Page 2 of 10 pages
================================================================================

- -------- -----------------------------------------------------------------------
1        NAME OF REPORTING PERSON
         S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

         Amerada Hess Corporation

- -------- -----------------------------------------------------------------------
2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP                 (a)|_|
                                                                          (b)|_|

- -------- -----------------------------------------------------------------------
3        SEC USE ONLY


- -------- -----------------------------------------------------------------------
4        SOURCE OF FUNDS

         BK; OO

- -------- -----------------------------------------------------------------------
5        CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED            |_|
         PURSUANT TO ITEMS 2(d) or 2(e)

- -------- -----------------------------------------------------------------------
6        CITIZENSHIP OR PLACE OF ORGANIZATION

         Delaware

- ----------------------------------- ------- ------------------------------------
NUMBER OF SHARES BENEFICIALLY       7       SOLE VOTING POWER
OWNED BY EACH REPORTING PERSON              None
WITH
                                    ------- ------------------------------------
                                    8       SHARED VOTING POWER
                                            21,968,313 (1)
                                    ------- ------------------------------------
                                    9       SOLE DISPOSITIVE POWER
                                            None
                                    ------- ------------------------------------
                                    10      SHARED DISPOSITIVE POWER
                                            21,968,313 (1)
- -------- -----------------------------------------------------------------------
11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         21,968,313 (1)
- -------- -----------------------------------------------------------------------
12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
         CERTAIN SHARES                                                      |_|


- -------- -----------------------------------------------------------------------
13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

         38.1% (2)
- -------- -----------------------------------------------------------------------
14       TYPE OF REPORTING PERSON

         CO
- -------- -----------------------------------------------------------------------


(1)  Based on (i) 1,733,573 ordinary shares and (ii) 5,058,685 8% convertible
     preference shares convertible into 4 ordinary shares each.

(2)  Based on (i) 37,500,375 ordinary shares and (ii) 5,058,685 8% convertible
     preference shares convertible into 4 ordinary shares each, all issued and
     outstanding as of July 5, 2001.





CUSIP No. G90751101 (Ordinary Shares)       Page 3 of 10 pages
================================================================================

- -------- -----------------------------------------------------------------------
1        NAME OF REPORTING PERSON
         S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

         Amerada Hess (Cayman) Limited

- -------- -----------------------------------------------------------------------
2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP                 (a)|_|
                                                                          (b)|_|
- -------- -----------------------------------------------------------------------
3        SEC USE ONLY


- -------- -----------------------------------------------------------------------
4        SOURCE OF FUNDS

         AF

- -------- -----------------------------------------------------------------------
5        CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
         PURSUANT TO ITEMS 2(d) or 2(e)                                      |_|

- -------- -----------------------------------------------------------------------
6        CITIZENSHIP OR PLACE OF ORGANIZATION

         Cayman Islands

- ----------------------------------- ------- ------------------------------------
NUMBER OF SHARES BENEFICIALLY        7      SOLE VOTING POWER
OWNED BY EACH REPORTING PERSON              None
WITH
                                    ------- ------------------------------------
                                     8      SHARED VOTING POWER
                                            21,968,313 (1)(3)
                                    ------- ------------------------------------
                                     9      SOLE DISPOSITIVE POWER
                                            None
                                    ------- ------------------------------------
                                     10     SHARED DISPOSITIVE POWER
                                            21,968,313 (1)(3)
- -------- -----------------------------------------------------------------------
11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         21,968,313 (1)(3)
- -------- -----------------------------------------------------------------------
12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
         CERTAIN SHARES                                                      |_|

- -------- -----------------------------------------------------------------------
13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

         38.1% (2)(3)
- -------- -----------------------------------------------------------------------
14       TYPE OF REPORTING PERSON

         CO
- -------- -----------------------------------------------------------------------


(1)  Based on (i) 1,733,573 ordinary shares and (ii) 5,058,685 8% convertible
     preference shares convertible into 4 ordinary shares each.

(2)  Based on (i) 37,500,375 ordinary shares and (ii) 5,058,685 8% convertible
     preference shares convertible into 4 ordinary shares each, all issued and
     outstanding as of July 5, 2001.

(3)  Amerada Hess (Cayman) Limited may be deemed to be the beneficial owner of
     the ordinary shares beneficially owned by Amerada Hess Corporation, its
     parent corporation, reported herein. Such shares of Amerada Hess (Cayman)
     Limited are included above.


CUSIP No. G90751101 (Ordinary Shares)                         Page 4 of 10 pages
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     This  statement  on  Schedule  13D (this  "Schedule  13D")  relates  to the
Acquisition  Agreement,  dated as of July 9, 2001, as amended (the  "Acquisition
Agreement")  by and among  Amerada  Hess  Corporation,  a  Delaware  corporation
("Amerada  Hess"),  Amerada Hess (Cayman)  Limited,  a company limited by shares
organized under the laws of the Cayman Islands  ("Purchaser")  and Triton Energy
Limited,  a company  limited  by shares  organized  under the laws of the Cayman
Islands (the "Company").  Pursuant to the Acquisition Agreement the Purchaser is
making an offer (the  "Offer") to purchase all of the  existing  unconditionally
allotted or issued and fully paid ordinary shares, par value $0.01 per share, of
the Company, and any further ordinary shares which are unconditionally  allotted
or issued  and fully paid  before the date and time on which the Offer  expires,
including the associated Series A junior participating  preferred share purchase
rights (the "Ordinary Shares").

     This  Schedule 13D also relates to the  Principal  Shareholders  Agreement,
dated as of July 9, 2001,  among the Purchaser,  Amerada Hess, the Company,  HM4
Triton,  L.P. and certain  other  shareholders  of the Company  (the  "Principal
Shareholders") who beneficially own, in the aggregate, 1,733,573 Ordinary Shares
and 5,058,685 8% convertible  preference  shares,  par value $0.01 per share, of
the Company (the "Preferred  Shares").  Each Preferred Share is convertible into
four Ordinary Shares. The Ordinary Shares and the Preferred Shares  beneficially
owned  by  the  Principal  Shareholders  represent  approximately  38.1%  of the
allotted and issued Ordinary Shares assuming conversion of such Preferred Shares
(34.2% on a fully  diluted  basis).  The Principal  Shareholders  have agreed to
tender pursuant to the Offer their Ordinary Shares and to conditionally  convert
their  Preferred  Shares  and  conditionally  tender  pursuant  to the Offer the
Ordinary Shares into which the Preferred Shares are convertible. The Acquisition
Agreement  requires the Purchaser to accept for payment and pay for all Ordinary
Shares owned by the Principal Shareholders and all Ordinary Shares issuable upon
conversion of the Preferred  Shares owned by the Principal  Shareholders  if the
Purchaser  accepts for payment any Ordinary Shares pursuant to the Offer. If the
Ordinary  Shares  beneficially  owned by the Principal  Shareholders  (including
Ordinary  Shares  issuable  upon the  conditional  conversion  and tender of the
Preferred  Shares) are not purchased  pursuant to the Offer  (excluding for this
purpose any  Subsequent  Offering  Period (as defined in the Offer to  Purchase,
which  appears as Exhibit 1 to this Schedule 13D and is  incorporated  herein by
reference (the "Offer to Purchase"))),  the Purchaser will purchase the Ordinary
Shares and the Preferred Shares beneficially owned by the Principal Shareholders
following the expiration of the initial offering period (including any extension
thereof).  The purchase price for the Ordinary  Shares would be $45.00 per share
in cash and the  purchase  price for the  Preferred  Shares would be $180.00 per
share, plus any accumulated and unpaid dividends thereon, in cash.

Item 1.   Security and Issuer

          This  Schedule  13D  relates to the  Ordinary  Shares.  The  principal
executive  offices of the  Company  are  located at  Caledonian  House,  Jennett
Street, P.O. Box 1043, George Town, Grand Cayman, Cayman Islands.




CUSIP No. G90751101 (Ordinary Shares)                         Page 5 of 10 pages
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Item 2.   Identity and Background

          This  Schedule 13D is being filed by Amerada  Hess and the  Purchaser.
The  information  set forth in the  section  of the Offer to  Purchase  entitled
Section 8. --"Certain Information Concerning the Purchaser and Amerada Hess" and
in Schedule I to the Offer to Purchase is  incorporated  herein by reference.

Item 3.   Source and Amount of Funds or Other Consideration

          The  information  set forth in the  section  of the Offer to  Purchase
entitled  Section 9.  --"Source and Amount of Funds" is  incorporated  herein by
reference.

Item 4.   Purpose of the Transaction

          The  information  set forth in the  sections  of the Offer to Purchase
entitled  "Introduction,"  Section  7.  --"Certain  Information  Concerning  the
Company," Section 8. --"Certain Information Concerning the Purchaser and Amerada
Hess," Section 10.  --"Background  of the Offer," Section 11.  --"Purpose of the
Offer; Plans for the Company;  Certain Agreements," Section  12.--"Dividends and
Distributions"  and  Section  13.--"Effect  of the Offer on the  Market  for the
Shares;  Exchange Act  Registration" is incorporated  herein by reference.  This
Schedule 13D relates to the  transactions  contemplated  by (i) the  Acquisition
Agreement and (ii) the Principal Shareholders Agreement.

          Except as set forth in this Item 4, neither the  Purchaser nor Amerada
Hess has any plans or  proposals  which  relate to or would result in any of the
actions specified in clauses (a) through (j) of Item 4 of Schedule 13D.

Item 5.   Interest in Securities of the Issuer

          (a) As a result of the Principal Shareholders Agreement, the Purchaser
and  Amerada  Hess may be  deemed  to be the  beneficial  owners  of  21,968,313
Ordinary Shares, consisting of 1,733,573 Ordinary Shares and 5,058,685 Preferred
Shares  each  convertible  into  4  Ordinary  Shares,  which  represents  in the
aggregate  approximately  38.1%  of the  allotted  and  issued  Ordinary  Shares
assuming  conversion of such Preferred  Shares (34.2% on a fully diluted basis).
The information set forth in Schedule I of the Offer to Purchase is incorporated
herein by reference.

          (b) The number of Ordinary Shares of the Company that may be deemed to
be beneficially  owned by each of the Purchaser and Amerada Hess with respect to
which  there is (i) sole  voting  power is none,  (ii)  shared  voting  power is
21,968,313,  (iii) sole dispositive  power is none, and (iv) shared  dispositive
power is  21,968,313.  The  information  set forth in Schedule I to the Offer to
Purchase is incorporated herein by reference.

          (c) The  information set forth in the section of the Offer to Purchase
entitled Section 8. --"Certain  Information Concerning the Purchaser and Amerada
Hess" is incorporated herein by reference.




CUSIP No. G90751101 (Ordinary Shares)                         Page 6 of 10 pages
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          (d) Not applicable.

          (e) Not applicable.

Item 6. Contracts, Arrangements, Understandings or Relationships with Respect to
        Securities of the Issuer

          The  information  set forth in the  sections  of the Offer to Purchase
entitled  "Introduction,"  Section 10.  --"Background of the Offer," Section 11.
- --"Purpose of the Offer; Plans for the Company;  Certain Agreements" and Section
8.  --"Certain  Information  Concerning  the  Purchaser  and  Amerada  Hess"  is
incorporated herein by reference.  A copy of the Joint Filing Agreement is filed
as Exhibit 7 to this Schedule 13D.

Item 7.    Material to Be Filed as Exhibits

Exhibit No.         Exhibit Name

1.                  Offer to Purchase, dated July 17, 2001. (1)

2.                  Third  Amended and Restated  Credit  Agreement,  dated as of
                    January 23, 2001,  among  Amerada  Hess,  the Lenders  Party
                    thereto and Goldman Sachs Credit Partners L.P. as joint book
                    runner,  joint lead  arranger  and sole  syndication  agent,
                    Chase  Securities,  Inc. as joint book runner and joint lead
                    arranger   and  The   Chase   Manhattan   Bank,   N.A.,   as
                    administrative  agent.  (2)

3.                  Third  Amended and Restated  Credit  Agreement,  dated as of
                    January 23, 2001,  among  Amerada  Hess,  the Lenders  Party
                    thereto and Goldman Sachs Credit Partners L.P. as joint book
                    runner,  joint lead  arranger  and sole  syndication  agent,
                    Chase  Securities,  Inc. as joint book runner and joint lead
                    arranger   and  The   Chase   Manhattan   Bank,   N.A.,   as
                    administrative agent. (3)

4.                  Acquisition  Agreement,  dated  as of July 9,  2001,  by and
                    among the  Purchaser,  Amerada Hess and the Company.  (4)

5.                  Amendment No. 1 to Acquisition  Agreement,  dated as of July
                    17, 2001, by and among the  Purchaser,  Amerada Hess and the
                    Company. (5)

6.                  Principal  Shareholders  Agreement dated as of July 9, 2001,
                    by and among the Purchaser,  Amerada Hess, the Company,  HM4
                    Triton,  L.P. and the Principal  Shareholders.  (6)

7.                  Joint Filing Agreement,  dated as of July 19, 2001,  between
                    the Purchaser and Amerada Hess.




CUSIP No. G90751101 (Ordinary Shares)                         Page 7 of 10 pages
================================================================================

(1)  Incorporated  by reference to Exhibit (a)(1) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(2)  Incorporated  by reference to Exhibit (b)(1) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(3)  Incorporated  by reference to Exhibit (b)(2) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(4)  Incorporated  by reference to Exhibit (d)(1) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(5)  Incorporated  by reference to Exhibit (d)(4) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(6)  Incorporated  by reference to Exhibit (d)(2) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.





CUSIP No. G90751101 (Ordinary Shares)                         Page 8 of 10 pages
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                                   SIGNATURES


          After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information  set forth in this statement is true,  complete and
correct.

Dated:  July 19, 2001




                                     AMERADA HESS CORPORATION



                                     By:   /s/ J. Barclay Collins II
                                        ----------------------------------------
                                        Name:   J. Barclay Collins II
                                        Title:  Executive Vice President
                                                and General Counsel




          After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information  set forth in this statement is true,  complete and
correct.

Dated:  July 19, 2001



                                     AMERADA HESS (CAYMAN) LIMITED



                                     By:   /s/ J. Barclay Collins II
                                        ----------------------------------------
                                        Name:   J. Barclay Collins II
                                        Title:  Director



CUSIP No. G90751101 (Ordinary Shares)                         Page 9 of 10 pages
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                                  EXHIBIT INDEX



Exhibit No.         Exhibit Name

1.                  Offer to Purchase, dated July 17, 2001. (1)

2.                  Third  Amended and Restated  Credit  Agreement,  dated as of
                    January 23, 2001,  among  Amerada  Hess,  the Lenders  Party
                    thereto and Goldman Sachs Credit Partners L.P. as joint book
                    runner,  joint lead  arranger  and sole  syndication  agent,
                    Chase  Securities,  Inc. as joint book runner and joint lead
                    arranger   and  The   Chase   Manhattan   Bank,   N.A.,   as
                    administrative agent. (2)

3.                  Third  Amended and Restated  Credit  Agreement,  dated as of
                    January 23, 2001,  among  Amerada  Hess,  the Lenders  Party
                    thereto and Goldman Sachs Credit Partners L.P. as joint book
                    runner,  joint lead  arranger  and sole  syndication  agent,
                    Chase  Securities,  Inc. as joint book runner and joint lead
                    arranger   and  The   Chase   Manhattan   Bank,   N.A.,   as
                    administrative agent. (3)

4.                  Acquisition  Agreement,  dated  as of July 9,  2001,  by and
                    among the Purchaser, Amerada Hess and the Company. (4)

5.                  Amendment No. 1 to Acquisition  Agreement,  dated as of July
                    17, 2001, by and among the  Purchaser,  Amerada Hess and the
                    Company. (5)

6.                  Principal  Shareholders  Agreement dated as of July 9, 2001,
                    by and among the Purchaser,  Amerada Hess, the Company,  HM4
                    Triton, L.P. and the Principal Shareholders. (6)

7.                  Joint Filing Agreement,  dated as of July 19, 2001,  between
                    the Purchaser and Amerada Hess.

(1)  Incorporated  by reference to Exhibit (a)(1) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(2)  Incorporated  by reference to Exhibit (b)(1) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(3)  Incorporated  by reference to Exhibit (b)(2) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(4)  Incorporated  by reference to Exhibit (d)(1) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(5)  Incorporated  by reference to Exhibit d(4) to the Tender Offer Statement on
     Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.

(6)  Incorporated  by reference to Exhibit (d)(2) to the Tender Offer  Statement
     on Schedule TO filed by Amerada Hess and the Purchaser on July 17, 2001.






CUSIP No. G90751101 (Ordinary Shares)                        Page 10 of 10 pages
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                                                                       Exhibit 7


                             JOINT FILING AGREEMENT

     This  confirms  the  agreement  by and  between  the  undersigned  that the
Statement  on Schedule  13D (the  "Statement")  filed on or about this date with
respect to the beneficial  ownership by the undersigned of the Ordinary  Shares,
par value $0.01, of Triton Energy Limited, a company limited by Shares organized
under the laws of the Cayman  Islands,  is being  filed on behalf of each of the
undersigned.

     Each of the undersigned hereby  acknowledges that pursuant to Rule 13d-1(k)
promulgated  under the  Securities  and Exchange Act of 1934,  as amended,  each
person on whose  behalf the  Statement  is filed is  responsible  for the timely
filing of such Statement and any amendments  thereto,  and for the  completeness
and accuracy of the information  concerning such person contained  therein;  and
that such  person is not  responsible  for the  completeness  or accuracy of the
information  concerning  the other person making the filing,  unless such person
knows or has reason to believe that such information is inaccurate.

     This Agreement may be executed in one or more  counterparts  by each of the
undersigned,  each of which,  taken together,  shall constitute one and the same
instrument.

Date:  July 19, 2001



                                         AMERADA HESS CORPORATION



                                         By:  /s/ J. Barclay Collins II
                                            ------------------------------------
                                            Name:     J. Barclay Collins II
                                            Title:    Executive Vice President
                                                      and General Counsel



                                         AMERADA HESS (CAYMAN) LIMITED



                                         By:  /s/ J. Barclay Collins II
                                            ------------------------------------
                                            Name:     J. Barclay Collins II
                                            Title:    Director