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 Cyberonics, each hereby certifies that:

     (a) the accompanying report on Form 10-Q for the quarter ended July 30, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”) by Cyberonics 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 Cyberonics.

Date: September 7, 2004

/s/ ROBERT P. CUMMINS  

Robert P. Cummins 

Chairman of the Board, Chief Executive Officer (Principal Executive Officer) and President 

/s/ PAMELA B. WESTBROOK  

Pamela B. Westbrook 

Vice President, Finance and Administration 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.