**EXHIBIT 31.1****CERTIFICATION**I, Daniel Jeffrey Moore, President and Chief Executive Officer of Cyberonics, Inc. certify that:     1. I have reviewed this Quarterly Report on Form 10-Q for the period ended July 27, 2007 ofCyberonics, Inc. (“the Registrant”);     2. Based on my knowledge, this report does not contain any untrue statement of a material factor omit to state a material fact necessary to make the statements made, in light of thecircumstances under which such statements were made, not misleading with respect to the periodcovered by this report;     3. Based on my knowledge, the financial statements, and other financial information includedin this report, fairly present in all material respects the financial condition, results ofoperations 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 andmaintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules13a-15(f) and 15d-15(f)) for the Registrant and have:     (a) Designed such disclosure controls and procedures, or caused such disclosurecontrols and procedures to be designed under our supervision, to ensure that materialinformation relating to the Registrant, including its consolidated subsidiary, is made knownto us by others within those entities, particularly during the period in which this reportis being prepared;     (b) Designed such internal control over financial reporting, or caused such internalcontrol over financial reporting to be designed under our supervision, to provide reasonableassurance regarding the reliability of financial reporting and the preparation of financialstatements for external purposes in accordance with generally accepted accountingprinciples;     (c) Evaluated the effectiveness of the Registrant’s disclosure controls and proceduresand presented in this report our conclusions about the effectiveness of the disclosurecontrols and procedures, as of the end of the period covered by this report based on suchevaluation; and     (d) Disclosed in this report any change in the Registrant’s internal control overfinancial reporting that occurred during the Registrant’s most recent fiscal quarter thathas materially affected, or is reasonably likely to materially affect, the Registrant’sinternal control over financial reporting; and     5. The Registrant’s other certifying officer and I have disclosed, based on our most recentevaluation of internal control over financial reporting, to the Registrant’s auditors and the auditcommittee 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 ofinternal control over financial reporting which are reasonably likely to adversely affectthe 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 whohave a significant role in the Registrant’s internal control over financial reporting.Date: August 30, 2007                                                          /s/ DANIEL JEFFREY MOORE    Daniel Jeffrey Moore    President and Chief Executive Officer