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                                  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

          Date of Report (Date of Earliest Event Reported): May 3, 2006
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                                HESS CORPORATION
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             (Exact Name of Registrant as Specified in Its Charter)

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

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

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

                            Amerada Hess Corporation
                          -----------------------------
                         (Former Name or Former Address,
                          If Changed Since Last Report)

     Check the appropriate box below if the Form 8-K filing is intended to
simultaneously satisfy the filing obligation of the registrant under any of the
following provisions (see General Instruction A.2. below):

  [ ]  Written communications pursuant to Rule 425 under the Securities Act
       (17 CFR 230.425)

  [ ]  Soliciting material pursuant to Rule 14a-12 under the Exchange Act
       (17 CFR 240.14a-2)

  [ ]  Pre-commencement communications pursuant to Rule 14d-2(b) under the
       Exchange Act (17 CFR 240.14d-2(b))

  [ ]  Pre-commencement communications pursuant to Rule 13e-4(c) under the
       Exchange Act (17 CFR 240.13e-4(c))

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ITEM 1.01   ENTRY INTO MATERIAL DEFINITIVE AGREEMENT.

     Effective May 3, 2006, following approval by its stockholders, Hess
Corporation (the "Company") adopted the Performance Incentive Plan for Senior
Officers (the "Plan"). The purpose of the Plan is to limit awards of incentive
cash compensation and restricted or deferred stock granted to the chief
executive officer and other designated senior officers in any year based on the
Company's financial performance for the preceding year. The terms and conditions
of the Plan are intended to assure that the awards will be deductible for
federal income tax purposes as qualified performance-based compensation under
section 162(m) of the Internal Revenue Code. Under the Plan, a participant's
combined awards of incentive cash compensation and restricted or deferred stock
for any year may not exceed a certain percentage (the participant's "maximum
awards percentage"), determined by the Company's Compensation and Management
Development Committee, of the Company's adjusted cash flow from operations for
the preceding year. The maximum awards percentage for any participant may not
exceed 1% of adjusted cash flow from operations for the preceding year and the
maximum awards percentage of all participants may not exceed 5% of adjusted cash
flow from operations for the preceding year. Adjusted cash flow from operations
for any year is defined as the excess of net cash provided by operating
activities (excluding changes in other operating assets and liabilities), as
shown in the statement of consolidated cash flows in the audited consolidated
financial statements of the Company for such year, over $550 million (unless the
committee specifies a higher amount).

ITEM 5.03   AMENDMENTS TO ARTICLES OF INCORPORATION OR BY-LAWS; CHANGE IN FISCAL
            YEAR.

     On May 3, 2006, following approval by its stockholders, the Company amended
its Restated Certificate of Incorporation to (i) change its name from "Amerada
Hess Corporation" to "Hess Corporation" and (ii) increase the total number of
shares of common stock which the Company has authority to issue from 200 million
shares to 600 million shares. A copy of the Certificate of Amendment of Restated
Certificate of Incorporation, as filed with the Secretary of State of the State
of Delaware on May 3, 2006, is attached hereto as Exhibit 3(1) and is hereby
incorporated by reference.

ITEM 9.01   FINANCIAL STATEMENTS AND EXHIBITS.

(d)    Exhibits

       3(1)  Certificate of Amendment of Restated Certificate of Incorporation,
              dated May 3, 2006.

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                                    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: May 4, 2006                          By:    /s/ J. Barclay Collins II
                                                  ------------------------------
                                           Name:  J. Barclay Collins II
                                           Title: Executive Vice President
                                                   and General Counsel

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EXHIBIT INDEX

Exhibit No.    Description
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3(1)          Certificate of Amendment of Restated Certificate of
               Incorporation, dated May 3, 2006.

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