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 June 26, 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: August 5, 2004                    By: /s/ Richard S. Hill
                                             -----------------------------------
                                             Richard S. Hill
                                             Chairman of the Board of Directors
                                             and Chief Executive Officer