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 Annual Report of General Motors Corporation (the
"Corporation") on Form 10-K for the period ended December 31, 2003 as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I, G.
Richard Wagoner, Jr., Chairman and Chief Executive Officer of the Corporation,
certify, pursuant to 18 U.S.C. ss. 1350, as adopted pursuant to ss. 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
     Corporation.


/s/ G. RICHARD WAGONER, JR.
- ---------------------------
G. Richard Wagoner, Jr.
Chairman and Chief Executive Officer
March 11, 2004



































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