EXHIBIT 32

                              CERTIFICATION OF THE
                           CHIEF EXECUTIVE OFFICER AND
                             CHIEF FINANCIAL OFFICER
                               OF CYBERONICS, INC.
                       PURSUANT TO 18 U.S.C. SECTION 1350

         Robert P. Cummins, the Chief Executive Officer of Cyberonics, Inc. (the
"Company"), and Pamela B. Westbrook, the Chief Financial Officer of the Company,
each hereby certifies that:

                  (a) the accompanying report on Form 10-Q for the quarter ended
         October 24, 2003 as filed with the Securities and Exchange Commission
         on the date hereof (the "Report") by the Company fully complies with
         the requirements of section 13(a) or 15(d) of the Securities Exchange
         Act of 1934 (15 U.S.C. 78m(a) or 78o(d)); and

                  (b) the information contained in the Report fairly presents,
         in all material respects, the financial condition and results of
         operations of the Company.

Date: December 4, 2003

                                /s/ ROBERT P. CUMMINS
                                -----------------------------------
                                Robert P. Cummins
                                Chairman of the Board, President and Chief
                                Executive Officer (Principal Executive Officer)

                                /s/ PAMELA B. WESTBROOK
                                -----------------------------------
                                Pamela B. Westbrook
                                Vice President, Finance and Administration,
                                Secretary and Chief Financial Officer (Principal
                                Financial and Accounting Officer)

         The certification set forth above is being submitted to the Securities
and Exchange Commission solely for the purpose of complying with Section 1350 of
Chapter 63 of Title 18 of the United States Code. This certification is not to
be deemed filed for purposes of Section 18 of the Securities Exchange Act of
1934, as amended, and does not constitute a part of the Report accompanying this
letter.

         A signed original of this written statement required by Section 906 has
been provided to Cyberonics, Inc. and will be retained by Cyberonics, Inc. and
furnished to the Securities and Exchange Commission or its staff upon request.