EXHIBIT 32.1

     CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of National-Oilwell, Inc. (the
"Company") on Form 10-Q for the period ending March 31, 2004 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), the
undersigned, Merrill A. Miller, Jr., Chairman, President and Chief Executive
Officer of the Company, hereby certifies, pursuant to 18 U.S.C. Section 1350, as
adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(i) The Report fully complies with the requirements of Section 13(a) of the
Securities Exchange Act of 1934; and

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

The certification is given to the knowledge of the undersigned.

        By:  /s/ Merrill A. Miller, Jr.
             --------------------------
        Name: Merrill A. Miller, Jr.
        Title: Chairman, President and Chief Executive Officer
        Date:  May 7, 2004

A signed original of this written statement required by Section 906, or other
document authenticating, acknowledging, or otherwise adopting the signature that
appears in typed form within the electronic version of this written statement
required by Section 906, has been provided to National-Oilwell, Inc. and will be
retained by National-Oilwell, Inc. and furnished to the Securities and Exchange
Commission or its staff upon request.

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