EXHIBIT 99.1

                             FIRST AMENDMENT TO THE
                            2001 STOCK INCENTIVE PLAN

      This First Amendment to the Nuevo Energy Company 2001 Stock Incentive Plan
(this "Amendment") was made and approved by the Board of Directors of Nuevo
Energy Company, a Delaware corporation (the "Company"), on October 29, 2002.

                                    RECITALS

      A. The Board of Directors of the Company approved and adopted the Nuevo
Energy Company 2001 Stock Incentive Plan on August 16, 2001 (the "Plan"); and

      B. The Board of Directors of the Company has approved the Amendment as
herein provided to increase the number of shares of common stock, par value $.01
per share, reserved for issuance under the Plan.

                                    AGREEMENT

      1. AMENDMENT TO THE AGGREGATE LIMITATION ON AWARDS. The second sentence of
Section 1.5(a) of the Plan shall be replaced with:

      "The maximum number of shares of Common Stock which may be issued pursuant
      to Awards issued under the Plan shall be 450,000 shares, which may be
      increased by the Board of Directors pursuant to Section 9.12."

      2. NO OTHER CHANGES. Except as explicitly amended by this Amendment, the
terms, conditions, rights and obligations under the Agreement shall remain in
full force and effect.

                                          /s/ Bruce K. Murchison
                                          Bruce K. Murchison, Secretary