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 J. Moore, President and Chief Executive Officer of Cyberonics, Inc. (the Company), and Gregory H. Browne, the Vice President, Finance and Chief Financial Officer of the Company, 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 24, 2015 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 20, 2015

/s/ DANIEL J. MOORE

Daniel J. Moore

President and Chief Executive Officer

(Principal Executive Officer)

/s/ GREGORY H. BROWNE

Gregory H. Browne

Senior Vice President, Finance and Chief Financial Officer

(Principal Financial Officer)