EXHIBIT 32.1

                                  Certification

      Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C.
1350), Stephen S. Schwartz, Chief Executive Officer of Asyst Technologies, Inc.
(the "Company"), and Robert J. Nikl, Chief Financial Officer of the Company,
each hereby certifies that, to the best of his knowledge:

      1. The Company's Quarterly Report for the period ended September 30, 2004,
to which this Certification is attached as Exhibit 32.1 (the "Periodic Report")
fully complies with the requirements of section 13(a) or section 15(d) of the
Securities Exchange Act of 1934, and

      2. The information contained in the Periodic Report fairly presents, in
all material respects, the financial condition and results of operations of the
Company.

Dated:  December 29, 2004

/s/ STEPHEN S. SCHWARTZ                              /S/ ROBERT J. NIKL
- -------------------------                            ------------------------
Stephen S. Schwartz, Ph.D.                           Robert J. Nikl
Chief Executive Officer                              Chief Financial Officer

This certification is not deemed to be "filed" for purposes of section 18 of the
Securities Exchange Act of 1934, or otherwise subject to the liability of that
section. This certification is not deemed to be incorporated by reference into
any filing under the Securities Act of 1933 or Securities Exchange Act of 1934,
except to the extent that the Company specifically incorporates it by reference.