SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549




                                    FORM 8-K



                                 CURRENT REPORT
                     PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934



                Date of Report (Date of Earliest Event Reported):
                                October 27, 2004




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



       DELAWARE                      No. 1-1204                  No. 13-4921002
    (State or Other                 (Commission                   (IRS Employer
   Jurisdiction of                  File Number)             Identification No.)
    Incorporation)




                           1185 Avenue of the Americas
                            New York, New York 10036
               (Address of Principal Executive Offices) (Zip Code)



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


                                       N/A
          (Former Name or Former Address, if Changed Since Last Report)



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Item 2.02.  Results of Operations and Financial Condition.

     On October 27, 2004, Amerada Hess Corporation issued a news release
reporting its results for the third quarter of 2004. A copy of this news release
is attached hereto as Exhibit 99(1) and is hereby incorporated by reference.


Item 9.01.  Financial Statements and Exhibits.

          (c)  Exhibits

          99(1) News release dated October 27, 2004 reporting results for the
                third quarter of 2004.

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                                    SIGNATURE


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

Date: October 27, 2004

                                       AMERADA HESS CORPORATION


                                       By:        /s/John P. Rielly
                                                  --------------------------
                                       Name:      John P. Rielly
                                       Title:     Senior Vice President and
                                                    Chief Financial Officer




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EXHIBIT INDEX


Exhibit No.         Description
-----------         -----------

99(1)               News release dated October 27, 2004 reporting results for
                    the third quarter of 2004.



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