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Exhibit 32.1

Written Statement of the Chief Executive Officer

        Pursuant to 18 U.S.C. Section 1350, I, the undersigned Chief Executive Officer of Genzyme Corporation (the "Company"), hereby certify that the Quarterly Report on Form 10-Q of the Company for the quarter ended March 31, 2004 (the "Report") fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/  HENRI A. TERMEER Henri A. Termeer
Chief Executive Officer
May 7, 2004

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Exhibit 32.1

Written Statement of the Chief Executive Officer