EXHIBIT 32.1

                          MCDERMOTT INTERNATIONAL, INC.

                            Certification Pursuant to
                  Section 906 of the Sarbanes-Oxley Act of 2002
        (Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18,
                               United States Code)

   Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a)
and (b) of Section 1350, Chapter 63 of Title 18, United States Code), I, Bruce
W. Wilkinson, Chairman of the Board and Chief Executive Officer of McDermott
International, Inc., a Panamanian corporation (the "Company"), hereby certify,
to my knowledge, that:

                  (1) the Company's Quarterly Report on Form 10-Q for the
                      quarter ended June 30, 2004 (the "Report") fully complies
                      with the requirements of Section 13(a) or 15(d) of the
                      Securities Exchange Act of 1934; and

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

Dated: August 9, 2004                                 \s\ Bruce W. Wilkinson
                                                      ----------------------
                                                      Bruce W. Wilkinson

                                                      Chairman of the Board and
                                                      Chief Executive Officer