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                       SECURITIES AND EXCHANGE COMMISSION

                              WASHINGTON, DC 20549


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                                    FORM 8-K

                                 CURRENT REPORT
                     PURSUANT TO SECTION 13 OR 15(D) OF THE
                         SECURITIES EXCHANGE ACT OF 1934


Date of report:                             JUNE 1, 2000
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Date of earliest event reported:            MAY 31, 2000
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                         DIAMOND OFFSHORE DRILLING, INC.
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               (Exact Name of Registrant as Specified in Charter)



DELAWARE                                1-13926                    76-0321760
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(State or Other Jurisdiction   (Commission File Number)        (IRS Employer
of Incorporation)                                           Identification No.)


15415 KATY FREEWAY, HOUSTON, TEXAS                              77094
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(Address of Principal Executive Offices)                      (Zip Code)



Registrant's telephone number, including area code   (281) 492-5300
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                                 NOT APPLICABLE
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          (Former name or former address, if changed since last report)




                    INFORMATION TO BE INCLUDED IN THE REPORT

ITEM 5. OTHER EVENTS

        On May 31, 2000, Diamond Offshore Drilling, Inc., a Delaware corporation
(the "Company"), issued a press release announcing the Company's plans to begin
a private placement of its 20-year zero coupon convertible debentures.

        On June 1, 2000, the Company issued a press release announcing the
pricing of the Company's 20-year zero coupon convertible debentures.

        Filed herewith are both such press releases.



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ITEM 7. FINANCIAL STATEMENTS, PRO FORMA FINANCIAL INFORMATION AND EXHIBITS

         (c)      Exhibits.

     Exhibit number        Description
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         99.1              Press release of May 31, 2000
         99.2              Press release of June 1, 2000








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                                   SIGNATURES

        Pursuant to the requirements of the Securities Exchange Act of 1934, as
amended, the registrant has duly caused this report to be signed on its behalf
by the undersigned hereunto duly authorized.

                                             DIAMOND OFFSHORE DRILLING, INC.


                                             By: /s/ Gary T. Krenek
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                                                 Gary T. Krenek
                                                 Vice President and
                                                 Chief Financial Officer

Dated: June 1, 2000



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                                  EXHIBIT INDEX


     Exhibit number        Description
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         99.1              Press release of May 31, 2000
         99.2              Press release of June 1, 2000










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