Exhibit 99.1

For Release Thursday, May 27, 2004; 8:00 AM EDT

CYBERONICS REPORTS FINANCIAL RESULTS FOR Q4 AND FY 2004

HOUSTON, Texas, May 27, 2004 — Cyberonics, Inc. (NASDAQ:CYBX) today reported financial results for the fourth quarter and fiscal year ended April 30, 2004.

Net sales for the fourth quarter ended April 30, 2004 were $26.3 million compared to net sales of $27.8 million for the quarter ended April 25, 2003. Fourth quarter net sales included $23.0 million from the U.S. market and $3.3 million from international markets. U.S. net sales decreased by 8% and international net sales increased by 16%, as compared to the fourth quarter of last year.

Net sales for the fiscal year ended April 30, 2004 were $110.7 million compared to net sales of $104.5 million for the fiscal year ended April 25, 2003. Net sales included $100.2 million from the U.S. market and $10.5 million from international markets. U.S. and international net sales increased by 5% and 21%, respectively, as compared to last year.

Net loss for the fourth quarter ended April 30, 2004 was $1.2 million, or $0.05 per fully diluted share, compared to net income of $4.0 million or $0.17 per fully diluted share for the quarter ended April 25, 2003, decreasing by $5.3 million, or $0.22 per fully diluted share over the same period last year. Net income for the fiscal year ended April 30, 2004 totaled $6.8 million or $0.26 per fully diluted share, compared to net income of $5.2 million or $0.22 per share for the fiscal year ended April 25, 2003, increasing by $1.6 million, or $0.04 per share over last year.

Cash and cash equivalents on hand on April 30, 2004 were $58.4 million, increasing by $14.8 million over the $43.6 million in cash and cash equivalents on hand on April 25, 2003.

“In fiscal 2004, Cyberonics accomplished more of its mission to improve the lives of people touched by epilepsy, depression and other chronic disorders that may prove to be treatable with our patented therapy, vagus nerve stimulation,” commented Robert P. (“Skip”) Cummins, Cyberonics’ Chairman and Chief Executive Officer. “Specifically in 2004, Cyberonics (1) expanded its intellectual property portfolio and cranial nerve stimulation franchise, (2) strengthened its senior leadership team by hiring a new Vice President of Sales and Cyberonics’ first Vice President of Human Resources and Vice President and General Counsel, (3) increased the number of new epilepsy patient implants and the profit and cash contribution of the epilepsy business, (4) internally funded the ongoing development of the depression indication, the PMA-Supplement which will be reviewed by FDA’s Neurological Devices Advisory Panel on June 15, (5) continued to vertically integrate and improve the scalability of Cyberonics’ manufacturing operations, (6) developed and launched the higher valued Model 102R replacement generator and (7)

continued to collect long-term data from the Alzheimer’s Disease, anxiety and chronic headache pilot studies and explore strategic alliances including out-licensing opportunities for other patented indications.”

“Cyberonics’ epilepsy business is now a $110 million annual sales, increasingly profitable and cash flow positive business that is internally funding all growth in epilepsy and other new indications,” continued Mr. Cummins. “In 2004, worldwide sales increased $6.3 million (6%), worldwide epilepsy contribution (net income plus direct new indication expenses) increased by $3.0 million (23%) and cash increased $14.8 million (34%). With or without an approved depression indication, we anticipate that worldwide annual epilepsy sales growth going forward will be similar to actual 2004 growth and that epilepsy growth will be largely driven by approximately $180 million of total end-of-service generator replacement sales through 2010. We also anticipate that epilepsy cash and profit contributions will continue to grow consistent with improving efficiencies in sales and manufacturing, and the over 90% gross margin associated with generator replacement sales.”

“On June 15, 2004, FDA’s Neurological Devices Advisory Panel will review Cyberonics’ PMA-Supplement seeking approval to market the VNS TherapyTM System “as an adjunctive long-term treatment of chronic or recurrent depression for patients over the age of 18 who are experiencing a major depressive episode that has not had an adequate response to two or more adequate antidepressant treatments,” added Mr. Cummins. “Our goal on June 15 is to present the long-term clinical data and analyses on approximately 460 patients in our depression studies and demonstrate to the Advisory Panel that: (1) treatment resistant depression (TRD) is a life-long, life-threatening illness that takes an enormous toll on patients, families, clinicians, hospitals, payers, employers, etc., (2) there is no FDA-approved, informed use, effective and tolerable long-term treatment for TRD and therefore there is a significant unmet need, (3) VNS is safe based on 29,000 patients and 72,000 patient years of experience in epilepsy and approximately 350 patients and 700 patient years of experience in the depression studies, and (4) VNS is effective as an adjunctive long-term treatment based on data and analyses from the acute placebo-controlled phase of the D-02 pivotal study, the one year longitudinal, patients-as-their-own-controls phase of the D-02 pivotal study and the comparison of the outcomes of the D-02 patients treated with VNS plus treatment-as-usual to the D-04 active control patients treated only with treatment-as-usual. At the conclusion of the Advisory Panel Meeting, we will know by the Advisory Panel’s vote whether or not we accomplished our objective. Regardless of whether the vote is in favor of or against approval, the next step in the process will be for us to meet with FDA before we finalize or announce a revised depression plan. We anticipate that we will announce such a revised plan in mid-August.”

“Considering the significant impact of upcoming events on our organization and financial performance, we will provide guidance for FY05 one quarter at a time,” commented Pamela B. Westbrook, Cyberonics’ Vice President, Finance & Administration and Chief Financial Officer. “For the first quarter, we expect that sales of $26.3 million will be sequentially flat as compared to Q4 sales and down slightly from Q1 of fiscal 2004 due to continuing decreases in end of service generator replacement sales. We are rapidly approaching the last of the Model 100 replacements and we do not expect to see meaningful Model 101 replacements until the last half of this year. We expect the first quarter net loss to be approximately $3.3 million or $0.14 per fully diluted share including approximately $3.5 million of new indications expenses. We will provide guidance for the second quarter in the first quarter financial results press release and

conference call that will occur in August. We do not anticipate needing any additional outside capital in FY05 with or without approval in depression.”

CONFERENCE CALL
A simultaneous conference call and Internet presentation to discuss fourth quarter and fiscal year 2004 results will occur at 8:30 AM EDT on Thursday, May 27, 2004. Two separate phone lines are necessary to access the conference call and Internet presentation. The audio portion of the conference call may be accessed by dialing 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 7544613; the leader is Pam Westbrook. A replay of the audio portion of the conference call will be available two hours after the completion of the conference call on Thursday, May 27, 2004 through June 10, 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 7544613.

You may access the Cyberonics Internet presentation site via the PresentPLUS Gateway address http://www.presentplus.com/conference/gatewaygold.html. To test your system in advance, take the instant system check by clicking on “Attendee Connectivity Check.” If you encounter difficulty, email support@presentplus.com with your telephone number for a call back. Once proper compatibility is confirmed, the presentation site can be accessed 10 minutes prior to the scheduled start, beginning at 8:20 AM EDT on Thursday, May 27 2004. Click on the link http://www.presentplus.com/conference/gatewaygold.html, then click on “Attendee Login” from the available options. Enter the Room Number of xcyberonics along with your name, company and e-mail address. You will then see a preview slide show. When the presenter is ready to begin, you will be connected to the main show.

HISTORY OF VNS THERAPY DEPRESSION STUDIES
Cyberonics’ comprehensive VNS Therapy depression study program began with the first pilot study implant in July 1998. The depression study program includes the following studies: a 60-patient acute and long-term pilot study (D-01); a 235-patient double blind, randomized, placebo controlled 8-week fixed dose acute pivotal study with a long-term extension (D-02); a 127-patient long-term observational study of patients with chronic or recurrent treatment resistant depression treated only with treatment as usual (D-04); neuroimaging, neurochemical and sleep mechanism of action studies; and several healthcare utilization and cost effectiveness studies. The patients in these studies were suffering from chronic or recurrent treatment resistant depression. In the D-02 and D-04 studies, the average lifetime illness exceeded 25 years and the average duration of the current depressive episode exceeded 48 months.

Highly statistically and clinically significant acute and long-term response and remission rates were observed in the D-01 pilot study. The first implant in the D-02 pivotal study occurred in August 2000. In January 2002, Cyberonics announced that although clinically meaningful, the difference in the D-02 treatment and placebo group HRSD-24 response rates at the end of the eight-week fixed dose acute study was not statistically significant. In September 2002, after determining the likely contributors to the lack of statistical significance, Cyberonics submitted a revised, prospective long-term pivotal study analysis plan to FDA. That plan was

designed to determine the statistical and clinical significance of the long-term improvements from baseline in all D-02 study patients treated over a one-year period with VNS Therapy and treatment as usual and to determine the causal relationship between those outcomes and VNS Therapy by comparing those D-02 outcomes with the outcomes of the D-04 patients treated only with treatment as usual.

In January 2003, Cyberonics announced that the one-year data from its D-02 depression pivotal study, analyzed pursuant to the D-02 analysis plan submitted to the FDA in September 2002, showed statistically and clinically significant improvements compared to baseline. Statistical significance was determined using a repeated measures linear regression technique to analyze improvements from pre-treatment baseline in the 24-item Hamilton Rating Scale (HRSD-24) during one year of VNS Therapy. The HRSD-24 improvements observed over the first year were highly significant with a p-value < 0.001. The secondary measures of statistical significance showed similarly positive results. Clinical significance was determined by analyzing the percent of patients who showed a sustained HRSD-24 response between nine and 12 months of treatment with VNS Therapy. In the absence of published literature that defines a long-term success criterion, Cyberonics’ psychiatric clinical advisors suggested that a sustained response rate of approximately 30% would be significant. Approximately 30% of the patients from the original acute treatment group and 27% of all patients in the analysis showed a sustained response between months nine and 12.

In July 2003, Cyberonics announced that the preliminary one-year results from its D-02 VNS Therapy depression pivotal study and D-04 companion study of chronic and recurrent treatment resistant depression, analyzed pursuant to the D-02 analysis plan submitted to the U.S. Food and Drug Administration (FDA) in September 2002, showed a highly statistically significant causal relationship (p-value < 0.001) between VNS Therapy and the depression improvements from baseline observed in the D-02 VNS Therapy study. The causal relationship between VNS Therapy and the D-02 patients’ one-year outcomes was determined using a repeated measures linear regression analysis to compare depression improvements as measured by the Inventory of Depressive Symptomatology-Self Report (IDS-SR) over one year in 205 D-02 patients receiving VNS Therapy and treatment as usual with the IDS-SR outcomes of 124 patients in a companion study, D-04, receiving only treatment as usual. In D-04, patients with chronic or recurrent treatment resistant depression who met the critical D-02 inclusion criteria were treated with standard medical management at 13 total study sites including 12 of the 21 D-02 study sites. Statistically and clinically significant differences in the physician and patient reported D-02 and D-04 patients’ one-year response and remission rates were also observed. One-year response rates, defined as at least a 50% improvement in depression symptoms as measured by the IDS-SR and HRSD-24 (24 item clinician rated Hamilton Rating Scale for Depression) were 22% and 30%, respectively in D-02 and 12% and 13%, respectively in D-04. One-year remission rates, defined as the percentage of patients free of depressive symptoms after one year of treatment, were 15% and 17%, respectively in D-02 and 4% and 7%, respectively in D-04.

In October 2003, Cyberonics submitted an 87-volume PMA-Supplement (PMA-S) to the U.S. Food and Drug Administration (FDA) seeking approval to market the VNS Therapy System in the United States as an adjunctive long-term treatment of chronic or recurrent treatment-resistant depression. That PMA-S included acute and one-year data and analyses on approximately 335 patients treated with VNS plus treatment as

usual and approximately 125 patients treated only with treatment as usual. FDA accepted the depression PMA-S for filing on December 15, 2003. The official filing date for regulatory timeline purposes is October 27, 2003. A Neurological Devices Advisory Panel Meeting has been scheduled by FDA for June 15, 2004 to review the depression PMA-S.

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 Therapy 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 guidance for fiscal 2005 relating to anticipated sales, gross profit margin, operating expenses and earnings, investments in new indication development, net income, profits and earnings per share, maintaining and obtaining appropriate regulatory approvals, developing VNS as a treatment for depression, the timing and outcome of clinical studies, improving our business model, building shareholder value, improving our productivity and efficiencies and increasing our sales, improving our net earnings and return on equity. 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 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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CYBERONICS, INC.
CONDENSED CONSOLIDATED BALANCE SHEETS

	APRIL 30, 2004		APRIL 25, 2003
ASSETS
Current Assets Cash and cash equivalents	$	58,363,731	$	43,576,305
Accounts receivable, net		16,951,176		14,164,771
Inventories		7,793,856		6,206,687
Other current assets		2,663,299		1,344,777
Total Current Assets		85,772,062		65,292,540
Property and equipment, net and other assets		8,524,462		9,822,772
	$	94,296,524	$	75,115,312
LIABILITIES AND STOCKHOLDERS’ EQUITY
Current liabilities	$	25,316,045	$	26,462,243
Long term liabilities		—		141,066
Stockholders’ equity		68,980,479		48,512,003
	$	94,296,524	$	75,115,312

CYBERONICS, INC.
CONSOLIDATED STATEMENTS OF OPERATIONS

	14 WEEKS ENDED			13 WEEKS ENDED			53 WEEKS ENDED			52 WEEKS ENDED
	APRIL 30, 2004			APRIL 25, 2003			APRIL 30, 2004			APRIL 25, 2003
	(Unaudited)			(Unaudited)
Net sales	$	26,307,817		$	27,777,475		$	110,721,499		$	104,466,998
Cost of sales		3,589,785			4,124,486			16,295,562			16,066,229
Gross Profit		22,718,032			23,652,989			94,425,937			88,400,769
Operating Expenses:
Selling, general and administrative		18,822,926			15,411,549			70,597,149			65,842,238
Research and development		4,746,644			4,174,846			17,133,709			17,874,909
Total Operating Expenses		23,569,570			19,586,395			87,730,858			83,717,147
Earnings (loss) From Operations		(851,538	)		4,066,594			6,695,079			4,683,622
Interest income		138,942			101,347			469,924			471,213
Interest expense		(140,820	)		(93,554	)		(565,702	)		(413,192	)
Other income (expense), net		(316,857	)		61,340			390,997			572,851
Earnings (loss) before income taxes		(1,170,273	)		4,135,727			6,990,298			5,314,494
Income Tax provision		75,257			101,764			230,789			129,563
Net Earnings (loss)	$	(1,245,530	)	$	4,033,963		$	6,759,509		$	5,184,931
Basic earnings (loss) per share	$	(0.05	)	$	0.18		$	0.29		$	0.24
Diluted earnings (loss) per share	$	(0.05	)	$	0.17		$	0.26		$	0.22
Shares used in computing basic earnings per share		23,403,720			22,318,725			22,921,031			22,034,651
Shares used in computing diluted earnings per share		23,403,720			24,196,672			26,053,330			23,173,324