EXHIBIT 32.1


                                CERTIFICATION OF
                             CHIEF EXECUTIVE OFFICER
                         OF NEWFIELD EXPLORATION COMPANY
                 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 accompanying report on Form 10-Q for the quarterly period
ended March 31, 2004 filed with the Securities and Exchange Commission on the
date hereof (the "Report"), I, David A. Trice, President and Chief Executive
Officer of Newfield Exploration Company (the "Company"), hereby certify, to 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: April 29, 2004                                 /s/ DAVID A. TRICE
                                                     -----------------------
                                                         David A. Trice