EXHIBIT 32.1

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

     Daniel Jeffrey Moore, President and Chief Executive Officer of Cyberonics, Inc. (the “Company”), and Gregory H. Browne, the Chief Financial Officer of Cyberonics, Inc., each hereby certifies pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

     (a) the Company’s Quarterly Report on Form 10-Q for the period ended July 27, 2007 as filed with the Securities and Exchange Commission on the date hereof (the “Report”) fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; 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: August 30, 2007

/s/ DANIEL JEFFREY MOORE  

Daniel Jeffrey Moore 

President and Chief Executive Officer
(Principal Executive Officer) 

/s/ GREGORY H. BROWNE  

Gregory H. Browne  

Vice President, Finance and Chief Financial Officer
(Principal Financial Officer) 

4