EXHIBIT 32.1

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

      Each of the undersigned hereby certifies, pursuant to 18 U.S.C. Section
1350, in his capacity as an officer of Diamond Offshore Drilling, Inc. (the
"Company"), that, to his knowledge:

      (1) the Company's Annual Report on Form 10-K for the fiscal year ended
December 31, 2004, as filed with the U.S. Securities and Exchange Commission on
the date hereof (the "Report"), fully complies with the requirements of Section
13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Dated:  March 2, 2005

/s/ JAMES S. TISCH
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James S. Tisch,
Chief Executive Officer of the Company

/s/ GARY T. KRENEK
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Gary T. Krenek,
Chief Financial Officer of the Company