EXHIBIT
31.1
  
 CERTIFICATION
 
 I, Daniel
J. Moore, Chief Executive Officer, certify that:
 
 1. I have
reviewed this Annual Report Form 10-K for the fiscal year ended April 25, 2008
of Cyberonics, Inc. (the registrant);
 
 2. Based
on my knowledge, this report does not contain any untrue statement of a material
fact or omit to state a material fact necessary to make the statements made, in
light of the circumstances under which such statements were made, not misleading
with respect to the period covered by this report;
 
 3. Based
on my knowledge, the financial statements, and other financial information
included in this report, fairly present in all material respects the financial
condition, results of operations and cash flows of the registrant as of, and
for, the periods presented in this report;
 
 4. The
registrant’s other certifying officer and I are responsible for establishing and
maintaining disclosure controls and procedures (as defined in Exchange Act Rules
13a-15(e) and 15d-15(e)) and internal control over financial reporting (as
defined in Exchange Act Rules 13a-15(f) and 15d-5(f)) for the registrant and
have:
 
 (a)
Designed such disclosure controls and procedures, or caused such disclosure
controls and procedures to be designed under our supervision, to ensure that
material information relating to the registrant, including its consolidated
subsidiary, is made known to us by others within those entities, particularly
during the period in which this report is being prepared;
 
 (b)
Designed such internal control over financial reporting, or caused such internal
control over financial reporting to be designed under our supervision, to
provide reasonable assurance regarding the reliability of financial reporting
and the preparation of financial statements for external purposes in accordance
with generally accepted accounting principles;
 
 (c)
Evaluated the effectiveness of the registrant’s disclosure controls and
procedures and presented in this report our conclusions about the effectiveness
of the disclosure controls and procedures, as of the end of the period covered
by this report based on such evaluation; and
 
 (d)
Disclosed in this report any change in the registrant’s internal control over
financial reporting that occurred during the registrant’s most recent fiscal
quarter that has materially affected, or is reasonably likely to materially
affect, the registrant’s internal control over financial reporting;
and
 
 5. The
registrant’s other certifying officer and I have disclosed, based on our most
recent evaluation of internal control over financial reporting, to the
registrant’s auditors and the audit committee of the registrant’s board of
directors (or persons performing the equivalent functions):
 
 (a) All
significant deficiencies and material weaknesses in the design or operation of
internal control over financial reporting which are reasonably likely to
adversely affect the registrant’s ability to record, process, summarize and
report financial information; and
 
 (b) Any
fraud, whether or not material, that involves management or other employees who
have a significant role in the registrant’s internal control over financial
reporting.
 
 /s/
      DANIEL JEFFREY MOOREDaniel
      Jeffrey MoorePresident
      and Chief Executive Officer(Principal
      Executive Officer)
 Date:           June
24, 2008