Exhibit 32

CERTIFICATION OF CEO AND CFO PURSUANT TO

18 U.S.C. § 1350,

AS ADOPTED PURSUANT TO

§ 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Form 10-K of Xerox Corporation, a New York corporation (the “Company”), for the year ending December 31, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Anne M. Mulcahy, Chairman of the Board and Chief Executive Officer of the Company, and Lawrence A. Zimmerman, Senior Vice President and Chief Financial Officer of the Company, each hereby certifies, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, to the best of his/her knowledge, that:

(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/    ANNE M. MULCAHY        

Anne M. Mulcahy

Chief Executive Officer

February 22, 2005

/s/    LAWRENCE A. ZIMMERMAN        

Lawrence A. Zimmerman

Chief Financial Officer

February 22, 2005

This certification accompanies this Report pursuant to § 906 of the Sarbanes-Oxley Act of 2002 and shall not, except to the extent required by the Sarbanes-Oxley Act of 2002, be deemed filed by the Company for purposes of § 18 of the Securities Exchange Act of 1934, as amended.

A signed original of this written statement required by § 906 has been provided to Xerox Corporation and will be retained by Xerox Corporation and furnished to the Securities and Exchange Commission or its staff upon request.