EXHIBIT 32.1



                                CERTIFICATION OF
                             CHIEF EXECUTIVE OFFICER
                        OF OIL STATES INTERNATIONAL, INC.
           PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO
  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002 AND RULE 13a - 14(b) UNDER THE
                         SECURITIES EXCHANGE ACT OF 1934



         In connection with the Annual Report on Form 10-K for the annual period
ended December 31, 2004 filed with the Securities and Exchange Commission (the
"Report"), I, Douglas E. Swanson, President and Chief Executive Officer of Oil
States International, Inc. (the "Company"), hereby certify, 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.



                                          /s/ Douglas E. Swanson
                                          --------------------------------------
                                          Name: Douglas E. Swanson
                                          Date: March 1, 2005