Exhibit 32.1



                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER
                        OF OIL STATES INTERNATIONAL, INC.
                       PURSUANT TO 18 U.S.C. SECTION 1350


         In connection with the accompanying report of Form 10-K for the year
ended December 31, 2003 filed with the Securities and Exchange Commission on the
date hereof (the "Report"), I, Douglas E. Swanson, President and Chief Executive
Officer of Oil States International, Inc. (the "Company"), hereby certify, to my
knowledge, that:

     1.  The Report fully complies with the requirement 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 5, 2004


         This certification is furnished solely pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002 and shall not be deemed to be a part of the Report or
"filed" for any purpose whatsoever.