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 March 27, 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.

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