EXHIBIT 32.1

                             NOVELLUS SYSTEMS, INC.

                                  CERTIFICATION

In connection with the periodic report of Novellus Systems, Inc. (the "Company")
on Form 10-Q for the period ended September 25, 2004 as filed with the
Securities and Exchange Commission (the "Report"), I, Richard S. Hill, Chairman
of the Board of Directors and Chief Executive Officer of the Company, hereby
certify as of the date hereof, solely for purposes of Title 18, Chapter 63,
Section 1350 of the United States Code, that to the best of my knowledge:

      (1)   the Report fully complies with the requirements of Section 13(a) or
            15(d), as applicable, 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 at the dates and for the periods indicated.

Dated: November 4, 2004                   By: /s/ Richard S. Hill
                                              ----------------------------------
                                              Richard S. Hill
                                              Chairman of the Board of Directors
                                              and Chief Executive Officer