<PAGE>

                                                                    EXHIBIT 10.1

                              EMPLOYMENT AGREEMENT

         This Employment Agreement (the "Agreement"), entered into effective as
of October 27, 2003 (the "Effective Date"), by and between Cyberonics, Inc. (the
"Company") and Randal L. Simpson ("Employee").

                                   WITNESSETH:

         WHEREAS, the Company desires to secure the experience, abilities and
service of Employee by employing Employee upon the terms and conditions
specified herein; and

         WHEREAS, Employee is willing to enter into this Agreement upon the
terms and conditions specified herein;

         NOW, THEREFORE, in consideration of the premises, terms and provisions
set forth herein, the mutual benefits to be gained by the performance thereof
and other good and valuable consideration, the receipt and sufficiency of which
are hereby acknowledged, the parties hereto agree as follows:

         SECTION 1. Employment. The Company hereby employs Employee, and
Employee hereby accepts such employment, all upon the terms and conditions set
forth herein.

         SECTION 2. Term. Subject to the terms and conditions of this Agreement,
unless sooner terminated pursuant to Section 5 of this Agreement, Employee shall
be employed by the Company commencing on the Effective Date and terminating on
the close of business on the third anniversary of the Effective Date (the
"Term"). Termination of this Agreement shall not alter or impair any rights of
Employee (or his beneficiaries or heirs) with respects to payments, benefits or
other rights provided by the terms of this Agreement, arising before or after
the end of the Term.

         SECTION 3. Duties, Responsibilities and Location.

                           A.       Capacity. Employee shall serve as the Vice
                  President, Operations of the Company and shall report to the
                  Chief Executive Officer of the Company.

                           B.       Full-Time Duties. Employee shall devote his
                  full business time, attention and energies to the business of
                  the Company. Notwithstanding anything herein to the contrary,
                  Employee shall be allowed to (i) manage Employee's personal
                  investments and affairs and, (ii) with the written consent of
                  the Chief Executive Officer of the Company, serve on boards or
                  committees of civic or charitable organizations or trade
                  associations, provided that such activities do not materially
                  interfere with his performance of the duties and
                  responsibilities of his position specified in Section 3.A.

                           C.       Offices. Employee's primary place of work
                  shall be at the principle executive offices of the Company
                  located in the greater Houston, Texas

<PAGE>

                  metropolitan area, but Employee shall be required to travel on
                  a basis consistent with his position.

SECTION 4. Compensation.

                           A.       Base Salary. During the Term, Employee shall
                  receive an annual salary of $200,000 (the "Base Salary")
                  payable in accordance with the Company's general payroll
                  practices. Employee's Base Salary shall be reviewed prior to
                  the beginning of each fiscal year of the Company for increase
                  in the discretion of the Compensation Committee of the Board
                  of Directors ("Compensation Committee"); provided, however,
                  that the Base Salary, as it may be increased at any time, may
                  not thereafter be decreased.

                           B.       Annual Incentive Bonus. During the Term,
                  Employee shall be eligible to participate in the Annual CEO
                  Direct Reports Bonus Plan, with a target bonus of 50% of
                  Employee's annual Base Salary prorated for fiscal 2004 based
                  on Employee's start date. A bonus, if earned, shall be payable
                  as soon as reasonably practical following the completion of
                  the applicable fiscal year. Bonuses for Employee shall be
                  based on the achievement of such Company, departmental and/or
                  individual performance goals that may be established for the
                  applicable bonus year by the Compensation Committee.

                           C.       Annual Overachievement Bonus. During the
                  Term, Employee shall be eligible to participate in the Annual
                  CEO Direct Reports Overachievement Bonus Plan as determined by
                  the Compensation Committee. Overachievement Bonuses shall be
                  based on the Company's overachievement of the annual Net
                  Sales, Earnings per Share and Cash Flow objectives included in
                  the annual budget approved by the Board of Directors at the
                  beginning of each year.

                           D.       Equity Compensation. Employee will be
                  eligible for grants of Company stock options (the "Options")
                  and other equity awards in the discretion of the Compensation
                  Committee.

                           E.       General Benefits. Upon satisfying applicable
                  eligibility requirements, if any, Employee will be eligible to
                  participate in the Company's qualified 401(k) plan, group
                  health, group life insurance, accidental death and
                  dismemberment, travel accident, long-term disability and
                  short-term disability plans and other welfare and similar
                  plans and vacation policies under terms generally applicable
                  to other similarly situated employees of the Company and shall
                  be eligible to receive all perquisites and other benefits
                  provided or made available by the Company to other similarly
                  situated executives of the Company.

                           F.       Reimbursements. Employee shall be entitled
                  to receive prompt reimbursement by the Company in accordance
                  with its business reimbursement policy in effect from time to
                  time for all reasonable, out-of-pocket business expenses
                  incurred by him in performing his duties under this Agreement
                  upon the

                                       -2-
<PAGE>

                  submission by Employee of such accounts and records as may be
                  reasonably required under the Company's business reimbursement
                  policy.

         SECTION 5. Termination of Employment. Notwithstanding the provisions of
Section 2, Employee's employment hereunder may terminate under any of the
following conditions:

                           A.       Death. Employee's employment under this
                  Agreement shall terminate automatically upon his death.

                           B.       Disability. Employee's employment under this
                  Agreement may be terminated due to his Disability.
                  "Disability" shall mean Employee's inability to substantially
                  perform his duties hereunder for any period of at least 180
                  consecutive days due to a physical or mental incapacity. The
                  date of termination due to Disability shall be the date
                  Employee elects to terminate his employment service due to
                  such Disability or, if earlier, the date the Board determines
                  that Employee has met the definition of Disability and given
                  written notice of such termination to Employee.

                           C.       Termination by Company Without Cause. The
                  Company may terminate Employee's employment hereunder without
                  Cause (as hereinafter defined) on 30 days' prior written
                  notice to Employee.

                           D.       Termination by Company for Cause. Employee's
                  employment hereunder may be terminated for Cause by the
                  Company. For purposes of this Agreement, "Cause" shall mean
                  (i) the willful and continued failure by Employee to
                  substantially perform Employee's duties with the Company
                  (other than any such failure resulting from Employee's
                  incapacity due to physical or mental illness), (ii) an act or
                  acts of dishonesty taken by Employee and intended to result in
                  personal enrichment of Employee at the expense of the Company,
                  (iii) willful violation by Employee of Employee's material
                  obligations under this Agreement, (iv) willful violation by
                  Employee of a material policy of the Company, including its
                  policies regarding professional and ethical conduct, (v)
                  Employee's commission of one or more acts that constitute a
                  felony, (vi) Employee is publicly censured by the Securities
                  Exchange Commission, or (vii) Employee commits one or more
                  acts of fraud as regards the Company. For purposes of clause
                  (i) of this definition, no act, or failure to act, on
                  Employee's part shall be deemed "willful" unless done, or
                  omitted to be done, by Employee not in good faith and without
                  reasonable belief that Employee's act, or failure to act, was
                  in the best interest of the Company. The determination of
                  whether Cause exists must be made by a resolution duly adopted
                  by the affirmative vote of not less than a majority of the
                  entire membership of the Board of Directors of the Company.

                           E.       Termination by Employee. Employee may
                  terminate his employment hereunder at any time on 30 days'
                  prior written notice to the Board.

                                       -3-
<PAGE>

         SECTION 6. Payments Upon Termination.

                           A.       Upon termination of Employee's employment
                  for any reason prior to the expiration of the Term, the
                  Company shall be obligated to pay, and Employee shall be
                  entitled to receive:

                                    1.       all accrued and unpaid Base Salary
                           to the date of termination;

                                    2.       any earned, but unpaid, bonuses for
                           the bonus year ending prior to the date of
                           termination;

                                    3.       all incurred but unreimbursed
                           business expenses for which Employee is entitled to
                           reimbursement; and

                                    4.       any benefits to which he is
                           entitled under the terms of any applicable employee
                           benefit plan or program, or applicable law.

                           B.       Upon termination of Employee's employment
                  pursuant to Section 5.C., the Company shall be obligated to
                  pay or provide, and Employee's estate or beneficiary shall be
                  entitled to receive:

                                    1.       all of the amounts and benefits
                           described in Section 6.A.; and

                                    2.       either (a) a lump sum payment equal
                           to 1.5 times the sum of (i) Employee's Base Salary,
                           plus (ii) the most recent annual bonus earned by
                           Employee or (b) a lump sum payment equal to 1.5 times
                           Employee's Base Salary and, solely for purposes of
                           determining Employee's vesting under any Options, the
                           number of shares that would become vested under such
                           Options during the 12-month period following
                           Employee's termination date if Employee's employment
                           had continued during such period shall become vested
                           on his termination of employment date, whichever of
                           (a) or (b) is elected by Employee in writing to the
                           Company within five days of his termination date.

                           C.       In the event of any termination of
                                    employment under Section 5, Employee shall
                  be under no obligation to seek other employment, and, except
                  as provided in Section 6.D, there shall be no offset against
                  amounts due Employee under this Agreement on account of any
                  remuneration attributable to any subsequent employment or
                  self-employment that he may obtain.

                           D.       If within two years of the Effective Date
                  either Employee terminates his employment with the Company
                  pursuant to Section 5.E. or the Company terminates Employee
                  pursuant to Section 5.D., Employee shall immediately repay to
                  the Company all unamortized relocation expenses paid by the
                  Company pursuant to Section 4.G., with such expenses amortized
                  on a straight-line basis over two years.

                                       -4-
<PAGE>

                           E.       The Company and Employee have previously or
                  contemporaneously with this Agreement entered into a Severance
                  Agreement which provides certain payments and benefits to
                  Employee upon a qualified termination of employment in
                  connection with a change of control of the Company.
                  Notwithstanding anything in this Agreement to the contrary, to
                  the extent Employee is entitled to receive any severance
                  payment or benefits under the Severance Agreement any
                  severance payment or benefits to which Employee is otherwise
                  entitled to receive under this Agreement shall be reduced or
                  offset by the severance payment or benefit payable under the
                  Severance Agreement in such manner as is appropriate, as
                  determined in good faith by the Board, to prevent a
                  duplication of such payment and benefits.

         SECTION 7. Indemnification. The Company agrees to indemnify Employee to
the fullest extent permitted by applicable law with respect to any acts or
non-acts he may have committed during the period which he was an officer,
director and/or employee of the Company or any subsidiary or affiliate thereof,
or of any other entity of which he served as an officer, director or employee at
the request of the Company.

         SECTION 8. Covenants of Employee. Employee covenants as follows:

                           A.       Confidentiality. During and after his
                  employment with the Company and its affiliates, Employee will
                  hold in confidence all confidential information and will not
                  disclose it to any person other than in connection with the
                  performance of his duties and obligations hereunder, except
                  with the specific prior written consent of the Board of
                  Directors or the Chief Executive Officer; provided, however,
                  that the parties agree that this Agreement does not prohibit
                  the disclosure of confidential information where applicable
                  law requires, including, but not limited to, in response of
                  subpoenas and/or orders of a governmental agency or court of
                  competent jurisdiction. In the event that Employee is
                  requested or becomes legally compelled under the terms of a
                  subpoena or order issued by a court of competent jurisdiction
                  or by a governmental body to make any disclosure of
                  confidential information, Employee agrees that he will (i)
                  immediately provide the Company with written notice of the
                  existence, terms and circumstances, surrounding such
                  request(s) so that the Company may seek an appropriate
                  protective order or other appropriate remedy, (ii) cooperate
                  with the Company in its efforts to decline, resist or narrow
                  such requests and (iii) if disclosure of such confidential
                  information is required in the opinion of counsel, exercise
                  reasonable efforts to obtain an order or other reliable
                  assurance that confidential treatment will be accorded to such
                  disclosed information. "Confidential information" means any
                  and all intellectual property of the Company (or any of its
                  affiliates), including but not limited to: (a) trade secrets
                  concerning the business and affairs of the Company (or any of
                  its affiliates), product specifications, data, know-how,
                  formulae, compositions, processes, designs, sketches,
                  photographs, graphs, drawings, samples, inventions and ideas,
                  past, current, and planned research and development, current
                  and planned manufacturing or distribution methods and
                  processes, customer lists, current and anticipated customer
                  requirements, price lists, market studies, business plans,

                                       -5-
<PAGE>

                  computer software and programs (including object code and
                  source code), computer software and database technologies,
                  systems, structures, and architectures (and related formulae,
                  compositions, processes, improvements, devices, know-how,
                  inventions, discoveries, concepts, ideas, designs, methods and
                  information), and any other information, however documented,
                  that is a trade secret under federal, state or other
                  applicable law; and (b) information concerning the business
                  and affairs of the Company (or any of its affiliates) (which
                  includes historical financial statements, financial
                  projections and budgets, historical and projected sales,
                  capital spending budgets and plans, the names and backgrounds
                  of key personnel, personnel training and techniques and
                  materials), however documented; and notes, analysis,
                  compilations, studies, summaries, and other material prepared
                  by or for the Company (or any of its affiliates) containing or
                  based, in whole or in part, on any information included in the
                  foregoing.

                           B.       Trade Secrets. Any trade secrets of the
                  Company will be entitled to all of the protections and
                  benefits under the federal and state trade secret and
                  intellectual property laws and any other applicable law. If
                  any information that the Company deems to be a trade secret is
                  found by a court of competent jurisdiction not to be a trade
                  secret for purposes of this Agreement, such information will,
                  nevertheless, be considered confidential information for
                  purposes of this Agreement, so long as it otherwise meets the
                  definition of confidential information. Employee hereby waives
                  any requirement that the Company submit proof of the economic
                  value of any trade secret or post a bond or other security.

                           C.       Proprietary Items. Employee will not remove
                  from the Company's premises (except to the extent such removal
                  is for purposes of the performance of Employee's duties at
                  home or while traveling, or except as otherwise specifically
                  authorized by the Company) any document, record, notebook,
                  plan, model, component, device, or computer software or code,
                  whether embodied in a disk or in any other form belonging to
                  the Company or used in the Company's business (collectively,
                  the "Proprietary Items"). All of the Proprietary Items,
                  whether or not developed by Employee, are the exclusive
                  property of the Company. Upon termination of his employment,
                  or upon the request of the Company during the Term, Employee
                  will return to the Company all of the Proprietary Items and
                  confidential information in Employee's possession or subject
                  to Employee's control, and Employee shall not retain any
                  copies, abstracts, sketches, or other physical embodiment,
                  including electronic or otherwise, of any of the Proprietary
                  Items or confidential information.

                           D.       Non-Competition and Non-Interference. During
                  the period of his employment with the Company or its
                  affiliates and for the one-year period after the termination
                  of his employment with the Company and its affiliates,
                  Employee will not, directly or indirectly:

                                    1.       without the express prior written
                           consent of the Board of Directors, own an interest
                           in, manage, operate, join, control, lend money

                                      -6-
<PAGE>

                           or render financial or other assistance to or
                           participate in or be connected with, as an officer,
                           employee, partner, stockholder, consultant or
                           otherwise, any person that competes with the Company
                           in the field of neurostimulation in a matter covered
                           by a patent assigned to or held by the Company;
                           provided, however, that following Employee's
                           termination of employment with the Company the
                           foregoing restriction shall apply only to those areas
                           where the Company is actually doing business on the
                           date of such termination of employment; provided,
                           further, that Employee may purchase or otherwise
                           acquire for passive investment up to 3% of any class
                           of securities of any such enterprise if such
                           securities are listed on any national or regional
                           securities exchange or have been registered under
                           Section 12(g) of the Securities Exchange Act of 1934;

                                    2.       whether for Employee's own account
                           or for the account of any other person, (except for
                           the account of the Company and its affiliates),
                           solicit Business from any person known by Employee to
                           be a customer of the Company or its affiliates,
                           whether or not Employee had personal contact with
                           such person during Employee's employment with the
                           Company and its affiliates;

                                    3.       whether for Employee's own account
                           or the account of any other person, (i) solicit,
                           employ, or otherwise engage as an employee,
                           independent contractor, or otherwise, any person who
                           is an employee of the Company or an affiliate, or in
                           any manner induce, or attempt to induce, any employee
                           of the Company or its affiliate to terminate his
                           employment with the Company or its affiliate; or (ii)
                           interfere with the Company's or its affiliate's
                           relationship with any person who at any time during
                           the Term, was an employee, contractor, supplier, or
                           customer of the Company or its affiliate; or

                                    4.       at any time after the termination
                           of his employment, disparage the Company or its
                           affiliates or any shareholders, directors, officers,
                           employees, or agents of the Company or any of its
                           affiliates, so long as the Company does not disparage
                           Employee.

                           E.       Acknowledgements. The Company acknowledges
                  that it is providing Employee with confidential information in
                  order for Employee to perform his duties under this Agreement.
                  Employee acknowledges that (a) the services to be performed by
                  him under this Agreement are of a special, unique, unusual,
                  extraordinary, and intellectual character, and (b) the
                  provisions of this Section 8 are reasonable and necessary to
                  protect the confidential information, goodwill and other
                  business interests of the Company. If any covenant in this
                  Section 8 is held to be unreasonable, arbitrary, or against
                  public policy, such covenant will be considered to be
                  divisible with respect to scope, time, and geographic area,
                  and such lesser scope, time, or geographic area, or all of
                  them, as a court of competent jurisdiction may determine to be
                  reasonable, not arbitrary, and not against public policy, will
                  be effective, binding, and enforceable against

                                      -7-
<PAGE>

                  Employee. Employee hereby agrees that this covenant is a
                  material and substantial part of this Agreement and that: (i)
                  the geographic limitations are reasonable; (ii) the term of
                  the covenant is reasonable; and (iii) the covenant is not made
                  for the purpose of limiting competition per se and is
                  reasonably related to a protectable business interest of the
                  Company. The period of time applicable to any covenant in this
                  Section 8 will be extended by the duration of any violation by
                  Employee of such covenant. The provisions of this Section 8
                  shall survive the termination of the Term of this Agreement.

         SECTION 9. Injunctive Relief and Additional Remedy. Employee
acknowledges that the injury that would be suffered by the Company as a result
of a breach of the provisions of Section 8 of this Agreement would be
irreparable and that an award of monetary damages to the Company for such a
breach would be an inadequate remedy. Consequently, the Company will have the
right, in addition to any other rights it may have, to obtain a temporary
restraining order and/or injunctive relief to restrain any breach or threatened
breach or otherwise to specifically enforce any provision of this Agreement.
Employee waives any requirement for the Company's securing or posting of any
bond in conjunction with any such remedies. Employee further agrees to and
hereby does submit to in personam jurisdiction before each and every court for
that purpose. Without limiting the Company's rights under this Section or any
other remedies of the Company, if Employee breaches any of the provisions of
Section 8 and such breach is proven in a court of competent jurisdiction, the
Company will have the right to cease making any payments or providing other
benefits otherwise due Employee under this Agreement.

         SECTION 10. Amendment; Waiver. The terms and provisions of this
Agreement may be modified or amended only by a written instrument executed by
each of the parties hereto, and compliance with the terms and provisions hereof
may be waived only by a written instrument executed by each party entitled to
the benefits thereof. No failure or delay on the part of any party in exercising
any right, power or privilege granted hereunder shall constitute a waiver
thereof, nor shall any single or partial exercise of any such right, power or
privilege preclude any other or further exercise thereof or the exercise of any
other right, power or privilege granted hereunder.

         SECTION 11. Entire Agreement. Except as contemplated herein and the
Severance Agreement referenced in Section 6.D., this Agreement constitutes the
entire agreement between the parties with respect to the subject matter hereof
and supersedes any and all prior or contemporaneous written or oral agreements,
arrangements or understandings between the Company and Employee.

         SECTION 12. Notices. All notices or communications hereunder shall be
in writing, addressed as follows or to any address subsequently provided to the
other party:

                To the Company:

                Cyberonics, Inc.
                Attention: Vice President of Human Resources
                100 Cyberonics Blvd., Suite 600
                Houston, Texas 77058

                                      -8-
<PAGE>

                To Employee:

                Randal L. Simpson
                3006 Cypress Point
                Missouri City, TX 77459

All such notices shall be conclusively deemed to be received and shall be
effective, (i) if sent by hand delivery or overnight courier, upon receipt, (ii)
if sent by telecopy or facsimile transmission, upon confirmation of receipt by
the sender of such transmission or (iii) if sent by registered or certified
mail, on the fifth day after the day on which such notice is mailed.

         SECTION 13. Severability. In the event that any term or provision of
this Agreement is found to be invalid, illegal or unenforceable, the validity,
legality and enforceability of the remaining terms and provisions hereof shall
not be in any way affected or impaired thereby, and this Agreement shall be
construed as if such invalid, illegal or unenforceable provision had never been
contained therein.

         SECTION 14. Binding Effect; Assignment. This Agreement shall be binding
upon and inure to the benefit of the parties and their respective successors and
assigns (it being understood and agreed that, except as expressly provided
herein, nothing contained in this Agreement is intended to confer upon any other
person or entity any rights, benefits or remedies of any kind or character
whatsoever). No rights or obligations of the Company under this Agreement may be
assigned or transferred by the Company except that such rights or obligations
may be assigned or transferred pursuant to a merger or consolidation in which
the Company is not the continuing entity, or the sale or liquidation of all or
substantially all of the assets of the Company, provided that the assignee or
transferee is the successor to all or substantially all of the assets of the
Company and such assignee or transferee assumes the liabilities, obligations and
duties of the Company, as contained in this Agreement, either contractually or
as a matter of law. The Company further agrees that, in the event of a sale of
assets or liquidation as described in the preceding sentence, it shall take
whatever action it legally can in order to cause such assignee or transferee to
expressly assume the liabilities, obligations and duties of the Company
hereunder.

         SECTION 15. Governing Law. This Agreement shall be governed by and
construed in accordance with the laws of the State of Texas (except that no
effect shall be given to any conflicts of law principles thereof that would
require the application of the laws of another jurisdiction).

         SECTION 16. Submission to Jurisdiction. EACH PARTY HEREBY IRREVOCABLY
SUBMITS TO THE EXCLUSIVE JURISDICTION OF THE STATE AND FEDERAL COURTS IN HARRIS
COUNTY, TEXAS, FOR THE PURPOSES OF ANY PROCEEDING ARISING OUT OF THIS AGREEMENT.

                                       -9-
<PAGE>

         SECTION 17. Headings. The headings of the sections contained in this
Agreement are for convenience only and shall not be deemed to control or affect
the meaning or construction of any provision of this Agreement.

         SECTION 18. Tax Withholdings. The Company shall withhold from all
payments hereunder all applicable taxes that it is required to withhold with
respect to payments and benefits provided under this Agreement.

         SECTION 19. Counterparts. This Agreement may be executed in one or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

         IN WITNESS WHEREOF, the undersigned have executed this Agreement
effective as of the date set forth above.

                                    CYBERONICS, INC.

                                    By: /s/ Robert P. Cummins
                                        ---------------------------------------
                                        Robert P. Cummins
                                        Chairman of the Board of Directors
                                        and Chief Executive Officer

                                    EMPLOYEE

                                    /s/ Randal L. Simpson
                                    -------------------------------------------
                                    Randal L. Simpson  Date : December 22, 2003

                                      -10-