EXHIBIT 32.1

                            CERTIFICATION 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 Quarterly Report on Form 10-Q of Nabors Industries Ltd.
(the "Company") for the quarter ended March 31, 2004 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, Eugene
M. Isenberg, Chairman and Chief Executive Officer of the Company, and I, Bruce
P. Koch, Vice President and Chief Financial Officer of the Company, each
certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906
of the Sarbanes-Oxley Act of 2002, that to the best of my knowledge:

      (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/ Eugene M. Isenberg
                                    --------------------------
                                    Eugene M. Isenberg
                                    Chairman and Chief Executive Officer
                                    May 7, 2004


                                    /s/ Bruce P. Koch
                                    --------------------------
                                    Bruce P. Koch
                                    Vice President and Chief Financial Officer
                                    May 7, 2004


A signed original of this written statement required by Section 906 of the
Sarbanes-Oxley Act of 2002 has been provided to Nabors Industries Ltd. and will
be retained by Nabors Industries Ltd. and will be furnished to the Securities
and Exchange Commission or its staff upon request.