EXHIBIT 32.1

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of Nuevo Energy Company (the "Company")
on Form 10-Q for the period ended June 30, 2003, as filed with the Securities
and Exchange Commission on the date hereof (the "Report"), I, James L. Payne,
President and Chief Executive Officer of the Company, certify, pursuant to 18
U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley
Act of 2002, to the best of my knowledge, that:


(1)    The Report fully complies with the requirements of Section 13(a) or
       15(d) of the Securities Exchange Act of 1934; and

(2)    The information contained in the Report fairly presents, in all material
       respects, the financial condition and results of operations of the
       Company.


Date:    August 13, 2003                     By:   /s/ James L. Payne
         --------------------------                -----------------------
                                                   James L. Payne
                                                   Chairman, President and
                                                   Chief Executive Officer

         This certification is being furnished solely for purposes of compliance
  with 18 U.S.C. Section 1350 and shall not be deemed "filed" for purposes of
  Section 18 of the Securities Exchange Act of 1934, as amended, or otherwise
  subject to the liabilities of that Section. Registration Statements or other
  documents filed with the Securities and Exchange Commission shall not
  incorporate this exhibit by reference, except as otherwise expressly stated in
  such filing.

         A signed original of this written statement required by Section 906 has
  been provided to Nuevo Energy Company and will be retained by Nuevo Energy
  Company and furnished to the Securities and Exchange Commission or its staff
  upon request.