EXHIBIT 32.1

CERTIFICATION OF 10-Q REPORT

OF

EXABYTE CORPORATION

FOR THE QUARTER ENDED MARCH 31, 2005

The undersigned are the Chief Executive Officer and the Chief Financial Officer of Exabyte Corporation (“Exabyte”). This Certification is made pursuant to Section 906 of the Sarbanes-Oxley Act of 2002. This Certification accompanies the 10-Q Report of Exabyte for the quarter ended March 31, 2005.

We certify that such 10-Q Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that the information contained in such 10-Q Report fairly presents, in all material respects, the financial condition and results of operations of Exabyte.

This Certification is executed as of May 12, 2005.

/s/ TOM W. WARD

Tom W. Ward

President and Chief Executive Officer

(Principal Executive Officer)

/s/ CARROLL A. WALLACE

Carroll A. Wallace

Chief Financial Officer, Treasurer

(Principal Financial and Accounting Officer)