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                                                                    EXHIBIT 32.1

                           AXCELIS TECHNOLOGIES, INC.

                  CERTIFICATION OF THE CHIEF EXECUTIVE OFFICER

  PURSUANT TO SECTION 1350 OF CHAPTER 63 OF TITLE 18 OF THE UNITED STATES CODE


The undersigned Chief Executive Officer of Axcelis Technologies, Inc., a
Delaware corporation, hereby certifies, for the purposes of Section 1350 of
Chapter 63 of title 18 of the United States Code (as implemented by Section 906
of the Sarbanes-Oxley Act of 2002) as follows:

This Form 10-K annual report fully complies with the requirements of section
13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d))
and the information contained herein fairly presents, in all material respects,
the financial condition and results of operations of the Company.

IN WITNESS WHEREOF, the undersigned has executed this Certification as of March
11, 2005.

                                       /s/ MARY G. PUMA
                                       -----------------------------------------
                                       Mary G. Puma
                                       Chief Executive Officer of Axcelis
                                       Technologies, Inc.

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