Exhibit 99.1

For Immediate Release Wednesday, September 15, 2004

FDA PROPOSES AND CYBERONICS SUBMITS TREATMENT IDE TO MAKE
VNS THERAPY^TM AVAILABLE TO A MUCH BROADER POPULATION

Conference call at 4:30 PM EDT today, September 15

HOUSTON, Texas, September 15, 2004 — Cyberonics, Inc. (NASDAQ:CYBX) today announced that it has submitted a Treatment IDE, at the suggestion of FDA’s Center for Devices and Radiological Health (CDRH), to make VNS Therapy available to patients with life-threatening treatment-resistant depression (TRD) in a multi-center, open-label, uncontrolled, longitudinal trial, while the FDA and Cyberonics continue to discuss the Company’s pending Expedited Review PMA-Supplement requesting approval to market VNS Therapy for chronic or recurrent treatment-resistant depression. In making this announcement, Cyberonics is responding to letters disclosing the Company’s IDE discussions with FDA, sent yesterday from Dr. Daniel Schultz, Director, Center for Devices & Radiological Health, to all patients and others who contacted FDA expressing their disappointment with FDA’s not-approvable decision. As stated in the FDA’s regulations (www.fda.gov/cdrh/devadvice/ide/early.shtml), the purpose of a Treatment IDE is to facilitate the availability of promising new devices to desperately ill patients, and a Treatment IDE is considered when (1) the device is intended to treat a serious or immediately life-threatening disease, (2) there is no comparable or satisfactory alternative device or other therapy to treat that stage of the disease or condition in the intended patient population, (3) the device is under investigation or the clinical trials have been completed for the same use, and (4) the sponsor is actively pursuing marketing approval/clearance of the device with due diligence.

“Cyberonics is pleased to work with FDA on a Treatment IDE to make VNS Therapy available to patients with treatment-resistant depression consistent with the proposed and Advisory Panel recommended use,” commented Robert P. (“Skip”) Cummins, Cyberonics’ Chairman of the Board and Chief Executive Officer. “We look forward to FDA’s timely approval of the Treatment IDE so Cyberonics can then begin the process of selecting treatment sites. Once sites are selected, the sites will obtain all requisite IRB (Institutional Review Board) approvals and patient informed consents. Although the Treatment IDE approval and implementation process will take time, and the Treatment IDE will provide only a limited number of TRD patients with VNS Therapy, it is, nonetheless, a step towards providing the millions of Americans with extreme TRD what they do not have today and what the FDA’s Advisory Panel recommended on June 15, 2004, and that is an informatively labeled treatment option developed and studied long-term specifically for TRD.

“More importantly, Cyberonics continues to work through an informal appeal process with CDRH to obtain FDA approval of our depression Expedited Review PMA-Supplement as recommended by FDA’s specially chosen Advisory Panel on June 15, 2004,” continued Mr. Cummins. “FDA’s not-approvable letter stated that ‘absent additional information’ our PMA-S must be considered not-approvable. We are working diligently with CDRH to

identify and submit additional compelling long-term data and analyses from the existing depression studies to address the concerns expressed in FDA’s not-approvable letter.”

CONFERENCE CALL ACCESS INFORMATION

A conference call to discuss this press release will be held at 4:30 PM EDT today, Wednesday, September 15, 2004. To listen to the conference call live by telephone dial 877-451-8943 (if dialing from within the U.S.) or 706-679-3062 (if dialing from outside the U.S.). The conference ID is 210644; the leader is Pam Westbrook. A replay of the conference call will be available two hours after the completion of the conference call on Wednesday, September 15, 2004 through Wednesday, September 29, 2004 by dialing 800-642-1687 (if dialing from within the U.S.) or 706-645-9291 (if dialing outside the U.S.). The replay conference ID access code is 210644.

ABOUT VNS THERAPY AND CYBERONICS

Cyberonics, Inc. (NASDAQ:CYBX) was founded in 1987 to design, develop and market medical devices for the long-term treatment of epilepsy and other chronic neurological disorders using a unique therapy, vagus nerve stimulation (VNS). Stimulation is delivered by the VNS TherapyTM System, an implantable generator similar to a cardiac pacemaker. The VNS Therapy System delivers preprogrammed intermittent mild electrical pulses to the vagus nerve 24 hours a day. The Company’s initial market is epilepsy, which is characterized by recurrent seizures. Epilepsy is the second most prevalent neurological disorder. The Cyberonics VNS Therapy System was approved by the FDA on July 16, 1997 for use as an adjunctive therapy in reducing the frequency of seizures in adults and adolescents over 12 years of age with partial onset seizures that are refractory to antiepileptic medications. The VNS Therapy System is also approved for sale as a treatment for epilepsy in all the member countries of the European Economic Area, Canada, Australia and other markets. To date, more than 29,000 epilepsy patients in 24 countries have accumulated over 72,000 patient years of experience using VNS Therapy. The VNS Therapy System is approved for sale in the European Economic Area and in Canada as a treatment for depression in patients with treatment-resistant or treatment-intolerant major depressive episodes including unipolar depression and bipolar disorder (manic depression). VNS Therapy is at various levels of investigational clinical study as a potential treatment for depression, anxiety disorders, Alzheimer’s disease, and chronic headache/migraine. The Company is headquartered in Houston, Texas and has an office in Brussels, Belgium. For additional information please visit us at www.cyberonics.com.

This press release contains forward-looking statements within the meaning of Section 27A of the Securities Act of 1933, as amended and Section 21E of the Securities Exchange Act of 1934, as amended. These statements can be identified by the use of forward-looking terminology, including “may,” “believe,” “will,” “expect,” “anticipate,” “estimate,” “plan,” “intend,” and “forecast,” or other similar words. Such forward-looking statements include statements concerning maintaining and obtaining appropriate regulatory approvals, developing VNS as a treatment for depression, the timing and outcome of clinical studies, the timing response and outcomes of our discussions with and submissions to FDA regarding approval of VNS as a treatment for depression and obtaining FDA approval of VNS for depression. Statements contained in this press release are based upon information presently available to us and assumptions that we believe to be reasonable. We are not assuming any duty to update this information should those facts change or should we no longer believe the assumptions to be reasonable. Our actual results may differ materially. Important factors that may cause actual results to differ include, but are not limited to: continued market

acceptance of VNS Therapy and sales of our product; the development and satisfactory completion of clinical trials and/or market test and/or regulatory approval of VNS Therapy for the treatment of depression, Alzheimer’s disease, anxiety, or other indications; adverse changes in coverage or reimbursement amounts by third-parties; intellectual property protection and potential infringement claims; maintaining compliance with government regulations and obtaining necessary government approvals for new applications; product liability claims and potential litigation; reliance on single suppliers and manufacturers for certain components; the accuracy of management’s estimates of future expenses and sales; and other risks detailed in from time to time in the Company’s filings with the SEC.

CONTACT INFORMATION:

Pamela B. Westbrook	Helen Shik
Vice President of Finance and CFO	Vice President
Cyberonics, Inc.	Schwartz Communications
100 Cyberonics Blvd.	230 Third Avenue
Houston, TX 77058	Waltham, MA 02154
Main: (281) 228-7200	Main: (781) 684-0770 ext. 6587
Fax: (281) 218-9332	Fax: (781) 684-6500
pbw@cyberonics.com	hshik@schwartz-pr.com

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