UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549



                                    FORM 8-K
                                 CURRENT REPORT
                       Pursuant to Section 13 and 15(d) of
                       the Securities Exchange Act of 1934



                                  June 2, 2004
                Date of Report (Date of earliest event reported)

                            AMERADA HESS CORPORATION
             (Exact Name of Registrant as Specified in Its Charter)


                                                                  13-4921002
        Delaware                       1-1204                   (IRS Employer
(State of Incorporation)      (Commission File Number)       Identification No.)


                           1185 Avenue of the Americas
                            New York, New York 10036
                     (Address of Principal Executive Office)


                                 (212) 997-8500
              (Registrant's Telephone Number, Including Area Code)


                                (Not Applicable)
                         (Former Name or Former Address,
                          If Changed Since Last Report)


Item 5.   OTHER EVENTS

          On June 2, 2004, the Board of Directors of Amerada Hess Corporation
(the "Company") elected as directors of the Company Dr. Risa Lavizzo-Mourey,
Chief Executive Officer and President of The Robert Wood Johnson Foundation, and
Mr. F. Borden Walker, Executive Vice President and President, Refining and
Marketing of the Company, to fill vacancies in the classes whose terms expire in
2006 and 2005, respectively.


                                    SIGNATURE

          Pursuant to the requirements of the Securities Exchange Act of 1934,
as amended, the Registrant has duly caused this report to be signed on its
behalf by the undersigned hereunto duly authorized.

                                        AMERADA HESS CORPORATION


DATE:  June 2, 2004                     By:   /s/ J. Barclay Collins II
                                           -------------------------------------
                                           Name:   J. Barclay Collins II
                                           Title:  Executive Vice President
                                                   and General Counsel