<PAGE>

                                                                    EXHIBIT 10.5

                            INDEMNIFICATION AGREEMENT

         This Indemnification Agreement (this "Agreement") is executed on and
effective as of November 13, 2001 (the "Effective Date"), by and between
Cyberonics, Inc., a Delaware corporation (the "Company"), and Thomas A. Duerden,
Ph.D. ("Director").

         WHEREAS, the Company and Director recognize the difficulty in obtaining
directors' and officers' liability insurance, the increases in the cost of such
insurance, and the general limitations in the coverage of such insurance;

         WHEREAS, the Company and Director further recognize the substantial
increase in corporate litigation in general, subjecting officers and directors
to expensive litigation risks at the same time as the availability and coverage
of liability insurance has been severely limited;

         WHEREAS, Director does not regard the current protection available as
adequate under the present circumstances, and Director and other officers and
directors of the Company may not be willing to serve or continue to serve as
officers and directors without additional protection; and

         WHEREAS, the Company desires to attract and retain the services of
highly qualified individuals, such as Director, to serve as officers and
directors of the Company and to indemnify its officers and directors so as to
provide them with the maximum protection permitted by law.

         NOW, THEREFORE, the Company and Director hereby agree as follows:

         1. Indemnification.

            a. Third Party Proceedings. The Company shall indemnify Director and
any partnership, corporation, trust, or other entity of which Director is or was
a partner, stockholder, trustee, director, officer, employee, or agent (Director
and each such partnership, corporation, trust, or other entity being referred to
as an "Indemnitee") if Indemnitee is or was a party or is threatened to be made
a party to any threatened, pending, or completed action, suit or proceeding,
whether civil, criminal, administrative, or investigative (other than an action
by or in the right of the Company) by reason of the fact that Director is or was
a director, officer, employee, or agent of the Company, or any subsidiary of the
Company, by reason of any action or inaction on the part of Director while an
officer or director or by reason of the fact that Director is or was serving at
the request of the Company as a director, officer, employee, or agent of another
corporation, partnership, joint venture, trust, or other enterprise, against
expenses (including attorneys' fees), judgments, fines, and amounts paid in
settlement (if such settlement is approved in advance by the Company, which
approval shall not be unreasonably withheld) actually and reasonably incurred by
Indemnitee in connection with such action, suit, or proceeding, if Director
acted in good faith and in a manner Director reasonably believed to be in or not
opposed to the best interests of the Company, and, with respect to any criminal
action or proceeding, had no reasonable cause to believe Director's conduct was
unlawful. The termination of any action, suit, or proceeding by judgment, order,
settlement, conviction, or upon a plea of nolo contendere or its equivalent,
shall not, of itself, create a presumption that Director did not act in good
faith and in a manner that Director reasonably believed to be in or not opposed
to the best interests of the Company, and, with respect to any criminal action
or proceeding, had reasonable cause to believe that Director's conduct was
unlawful.


<PAGE>


            b. Proceedings By or in the Right of the Company. The Company shall
indemnify Indemnitee if Indemnitee was or is a party or is threatened to be made
a party to any threatened, pending, or completed action or suit by or in the
right of the Company or any subsidiary of the Company to procure a judgment in
its favor by reason of the fact that Director is or was a director, officer,
employee, or agent of the Company, or any subsidiary of the Company, by reason
of any action or inaction on the part of Director while an officer or director
or by reason of the fact that Director is or was serving at the request of the
Company as a director, officer, employee, or agent of another corporation,
partnership, joint venture, trust, or other enterprise, against expenses
(including attorneys' fees) and, to the fullest extent permitted by law, amounts
paid in settlement, in each case to the extent actually and reasonably incurred
by Indemnitee in connection with the defense or settlement of such action or
suit, if Director acted in good faith and in a manner Director reasonably
believed to be in or not opposed to the best interests of the Company, except
that no indemnification shall be made in respect of any claim, issue, or matter
as to which Director shall have been adjudged to be liable to the Company unless
and only to the extent that the Court of Chancery of the State of Delaware or
the court in which such action or suit was brought shall determine upon
application that, despite the adjudication of liability but in view of all the
circumstances of the case, Indemnitee is fairly and reasonably entitled to
indemnity for such expenses that the Court of Chancery of the State of Delaware
or such other court shall deem proper.

            c. Mandatory Payment of Expenses. To the extent that Indemnitee has
been successful on the merits or otherwise in defense of any action, suit, or
proceeding referred to in Sections 1(a) and (b) or the defense of any claim,
issue, or matter therein, Indemnitee shall be indemnified against expenses
(including attorneys' fees) actually and reasonably incurred by Indemnitee in
connection therewith.

         2. Expenses: Indemnification Procedure.

            a. Advancement of Expenses. The Company shall advance all expenses
incurred by Indemnitee, and, to the fullest extent permitted by law, amounts
paid in settlement by Indemnitee, in connection with the investigation, defense,
settlement, or appeal of any civil or criminal action, suit, or proceeding
referenced in Section 1(a) or (b) hereof. Indemnitee hereby undertakes to repay
such amounts advanced only if, and to the extent that, it shall ultimately be
determined that Indemnitee is not entitled to be indemnified by the Company as
authorized hereby. The advances to be made hereunder shall be paid by the
Company to Indemnitee within 20 days following delivery of a written request
therefor by Indemnitee to the Company.

            b. Notice/Cooperation by Indemnitee. Indemnitee shall, as a
condition precedent to his or its right to be indemnified under this Agreement,
give the Company notice in writing as soon as practicable of any claim made
against Indemnitee for which indemnification will or could be sought under this
Agreement. Notice to the Company shall be directed to the President of the
Company at the address shown on the signature page of this Agreement, or such
other address as the Company shall designate in writing to Indemnitee. Notice
shall be deemed received three business days after the date postmarked if sent
by domestic certified or registered mail, properly addressed; otherwise notice
shall be deemed received when such notice shall actually be received by the
Company. In addition, Indemnitee shall give the Company such information and
cooperation as it may reasonably require and as shall be within Indemnitee's
power.


                                       2
<PAGE>


            c. Procedure. Any indemnification and advances provided for in
Section 1 and this Section 2 shall be made no later than 45 days after receipt
of the written request of Indemnitee. If a claim under this Agreement, under any
statute, or under any provision of the Company's Certificate of Incorporation or
Bylaws providing for indemnification, is not paid in full by the Company within
45 days after a written request for payment thereof has first been received by
the Company, Indemnitee may, but need not, at any time thereafter bring an
action against the Company to recover the unpaid amount of the claim and,
subject to Section 12 of this Agreement, Indemnitee shall also be entitled to be
paid for the expenses (including attorneys' fees) of bringing such action. It
shall be a defense to any such action (other than an action brought to enforce a
claim for expenses incurred in connection with any action, suit, or proceeding
in advance of its final disposition) that Indemnitee has not met the standards
of conduct that make it permissible under applicable law for the Company to
indemnify Indemnitee for the amount claimed, but the burden of proving such
defense shall be on the Company and Indemnitee shall be entitled to receive
interim payments of expenses pursuant to Subsection 2(a) unless and until such
defense may be finally adjudicated by court order or judgment from which no
further right of appeal exists. It is the parties' intention that if the Company
contests Indemnitee's right to indemnification, the question of Indemnitee's
right to indemnification shall be for the court to decide, and neither the
failure of the Company (including its Board of Directors, any committee or
subgroup of the Board of Directors, independent legal counsel, or its
stockholders) to have made a determination that indemnification of Indemnitee is
proper in the circumstances because Indemnitee has met the applicable standard
of conduct required by applicable law, nor an actual determination by the
Company (including its Board of Directors, any committee or subgroup of the
Board of Directors, independent legal counsel, or its stockholders) that
Indemnitee has not met such applicable standard of conduct, shall create a
presumption that Indemnitee has or has not met the applicable standard of
conduct.

            d. Notice to Insurers. If, at the time of the receipt of a notice of
a claim pursuant to Section 2(b) hereof, the Company has directors' and
officers' liability insurance in effect, the Company shall give prompt notice of
the commencement of such proceeding to the insurers in accordance with the
procedures set forth in the respective policies. The Company shall thereafter
take all necessary or desirable action to cause such insurers to pay, on behalf
of the Indemnitee, all amounts payable as a result of such proceeding in
accordance with the terms of such policies.

            e. Selection of Counsel. In the event the Company shall be obligated
under Section 2(a) hereof to pay the expenses of any proceeding against
Indemnitee, the Company, if appropriate, shall be entitled to assume the defense
of such proceeding, with counsel approved by Indemnitee (whose approval shall
not be unreasonably withheld), upon the delivery to Indemnitee of written notice
of its election so to do. After delivery of such notice, approval of such
counsel by Indemnitee and the retention of such counsel by the Company, the
Company will not be liable to Indemnitee under this Agreement for any fees of
counsel subsequently incurred by Indemnitee with respect to the same proceeding,
provided that (i) Indemnitee shall have the right to employ his counsel in any
such proceeding at Indemnitee's expense; and (ii) if (A) the employment of
counsel by Indemnitee has been previously authorized by the Company, (B)
Indemnitee shall have reasonably concluded that there may be a conflict of
interest between the Company and Indemnitee in the conduct of any such defense,
or (C) the Company shall not, in fact, have employed counsel to assume the
defense of such proceeding, then the fees and expenses of Indemnitee's counsel
shall be at the expense of the Company.


                                       3
<PAGE>


         3. Additional Indemnification Rights; Nonexclusivity.

            a. Scope. Notwithstanding any other provision of this Agreement, the
Company hereby agrees to indemnify the Indemnitee to the fullest extent
permitted by law, notwithstanding that such indemnification is not specifically
authorized by the other provisions of this Agreement, the Company's Certificate
of Incorporation, the Company's Bylaws, or by statute. In the event of any
change, after the date of this Agreement, in any applicable law, statute, or
rule that expands the right of a Delaware corporation to indemnify a member of
its board of directors or an officer, such changes shall be, ipso facto, within
the purview of Indemnitee's rights and Company's obligations under this
Agreement. In the event of any change in any applicable law, statute, or rule
that narrows the right of a Delaware corporation to indemnify a member of its
board of directors or an officer, such changes, to the extent not otherwise
required by such law, statute, or rule to be applied to this Agreement, shall
have no effect on this Agreement or the parties' rights and obligations
hereunder.

            b. Nonexclusivity. The indemnification provided by this Agreement
shall not be deemed exclusive of any rights to which Director or any other
Indemnitee may be entitled under the Company's Certificate of Incorporation, its
Bylaws, any agreement, any vote of stockholders or disinterested directors, the
General Corporation Law of the State of Delaware, or otherwise, both as to
action in Director's official capacity and as to action in another capacity
while holding such office. The indemnification provided under this Agreement
shall continue as to Director and each other Indemnitee for any action taken or
not taken while Director is or was serving in an indemnified capacity even
though he may have ceased to serve in such capacity at the time of any action,
suit, or other covered proceeding.

         4. Partial Indemnification. If Indemnitee is entitled under any
provision of this Agreement to indemnification by the Company for some or a
portion of the expenses, judgments, fines, or penalties actually or reasonably
incurred by Indemnitee in the investigation, defense, appeal, or settlement of
any civil or criminal action, suit, or proceeding, but not, however, for the
total amount thereof, the Company shall nevertheless indemnify Indemnitee for
the portion of such expenses, judgments, fines, or penalties to which Indemnitee
is entitled.

         5. Mutual Acknowledgment. Both the Company and Director acknowledge
that in certain instances Federal law or applicable public policy may prohibit
the Company from indemnifying its directors and officers under this Agreement or
otherwise, in which event, notwithstanding any other provisions of this
Agreement to the contrary, the indemnification provided by this Agreement shall
be limited to such extent as is necessary to comply with applicable Federal law
or public policy. For example, the Company and Director acknowledge that the
Securities and Exchange Commission (the "SEC") has taken the position that
indemnification is not permissible for liabilities arising under certain federal
securities laws, and federal legislation prohibits indemnification for certain
violations of the Employee Retirement Income Security Act of 1974, as amended
("ERISA"). Director understands and acknowledges that in the event the Company
undertakes a public offering of its securities pursuant to a registration with
the SEC, the Company may be required to undertake with the SEC to submit the
question of indemnification to a court in certain circumstances for a
determination of the Company's right under public policy to indemnify Director
or any other Indemnitee.


                                       4
<PAGE>


         6. Directors and Officers Liability Insurance. The Company has applied
for and will use its best efforts to obtain and maintain in force with a
financially sound and reputable insurer a directors, officers, and corporate
liability insurance policy having a limit which the Company, together with the
Board of Directors, approves as providing coverage appropriate and acceptable to
the Board of Directors. In all policies of directors and officers liability
insurance, Director and each other Indemnitee shall be named as an insured in
such a manner as to provide Director the same rights and benefits as are
accorded to the most favorably insured of the Company's directors.

         7. Severability. Nothing in this Agreement is intended to require or
shall be construed as requiring the Company to do or fail to do any act in
violation of applicable law. The Company's inability, pursuant to court order,
to perform its obligations under this Agreement shall not constitute a breach of
this Agreement. The provisions of this Agreement shall be severable as provided
in this Section 7. If this Agreement or any portion hereof shall be invalidated
on any ground by any court of competent jurisdiction, then the Company shall
nevertheless indemnify Director and each other Indemnitee to the full extent
permitted by any applicable portion of this Agreement that shall not have been
invalidated, and the balance of this Agreement not so invalidated shall be
enforceable in accordance with its terms.

         8. Exceptions. Any other provision herein to the contrary
notwithstanding, the Company shall not be obligated pursuant to the terms of
this Agreement:

            a. Claims Initiated by Indemnitee. To indemnify or advance expenses
to Indemnitee with respect to proceedings or claims initiated or brought
voluntarily by Indemnitee and not by way of defense, except with respect to
proceedings brought to establish or enforce a right to indemnification under
this Agreement or any other statute or law or otherwise as required under
Section 145 of the Delaware General Corporation Law, but such indemnification or
advancement of expenses may be provided by the Company in specific cases if the
Board of Directors finds it to be appropriate;

            b. Lack of Good Faith. To indemnify Indemnitee for any expenses
incurred by the Indemnitee with respect to any proceeding instituted by
Indemnitee to enforce or interpret this Agreement, if a court of competent
jurisdiction determines that each of the material assertions made by the
Indemnitee in such proceeding was not made in good faith or was frivolous;

            c. Insured Claims. To indemnify Indemnitee for expenses or
liabilities of any type whatsoever (including, but not limited to, judgments,
fines, ERISA, excise taxes or penalties, and amounts paid in settlement) that
have been paid directly to Indemnitee by an insurance carrier under a policy of
officers' and directors' liability insurance maintained by the Company; or

            d. Claims Under Section 16(b). To indemnify Indemnitee for expenses
and the payment of profits arising from the purchase and sale by Indemnitee of
securities in violation of Section 16(b) of the Securities Exchange Act of 1934,
as amended, or any similar successor statute.

         9. Construction of Certain Phrases.

            a. For purposes of this Agreement, references to the "Company" shall
include, in addition to the resulting corporation, any constituent corporation
(including any constituent of a constituent) absorbed in a consolidation or
merger, so that if Indemnitee is or was a director, officer,


                                       5
<PAGE>


employee, or agent of such constituent corporation, or is or was serving at the
request of such constituent corporation as a director, officer, employee, or
agent of another corporation, partnership, joint venture, trust, or other
enterprise, Indemnitee shall stand in the same position under the provisions of
this Agreement with respect to the resulting or surviving corporation as
Indemnitee would have with respect to such constituent corporation if its
separate existence had continued.

            b. For purposes of this Agreement, references to "other enterprises"
shall include employee benefit plans; references to "fines" shall include any
excise taxes assessed on Indemnitee with respect to an employee benefit plan;
and references to "serving at the request of the Company" shall include any
service as a director, officer, employee, or agent of the Company that imposes
duties on, or involves services by, such director, officer, employee, or agent
with respect to an employee benefit plan, its participants, or beneficiaries;
and if Indemnitee acted in good faith and in a manner Indemnitee reasonably
believed to be in the interest of the participants and beneficiaries of an
employee benefit plan, Indemnitee shall be deemed to have acted in a manner "not
opposed to the best interests of the Company" as referred to in this Agreement.

         10. Counterparts. This Agreement may be executed in one or more
counterparts, each of which shall constitute an original.

         11. Successors and Assigns. This Agreement shall be binding upon the
Company and its successors and assigns, and shall inure to the benefit of
Director and each other Indemnitee and their respective estates, heirs,
successors, legal representatives, and assigns.

         12. Attorneys' Fees. In the event that any action is instituted by
Indemnitee under this Agreement to enforce or interpret any of the terms hereof,
Indemnitee shall be entitled to be paid all court costs and expenses, including
reasonable attorneys' fees, incurred by Indemnitee with respect to such action,
unless as a part of such action, the court of competent jurisdiction determines
that each of the material assertions made by Indemnitee as a basis for such
action was not made in good faith or was frivolous. In the event of an action
instituted by or in the name of the Company under this Agreement or to enforce
or interpret any of the terms of this Agreement, Indemnitee shall be entitled to
be paid all court costs and expenses, including attorneys' fees, incurred by
Indemnitee in defense of such action (including with respect to Indemnitee's
counterclaims and cross-claims made in such action), unless as a part of such
action the court determines that each of Indemnitee's material defenses to such
action was made in bad faith or was frivolous.

         13. Notice. All notices, requests, demands, and other communications
under this Agreement shall be in writing and shall be deemed duly given on the
third business day after the date postmarked, if delivered by domestic certified
or registered mail with postage prepaid, or, if delivered by other means, on the
date actual notice is received. Addresses for notice to either party are as
shown on the signature page of this Agreement, or as subsequently modified by
written notice.

         14. Consent to Jurisdiction. The Company and Indemnitee each hereby
irrevocably consent to the non-exclusive jurisdiction of the courts of the State
of Delaware for all purposes in connection with any action or proceeding that
arises out of or relates to this Agreement and agree that any action instituted
under this Agreement may be brought in any court of competent jurisdiction in
the State of Delaware.


                                       6
<PAGE>


         15. CHOICE OF LAW. THIS AGREEMENT SHALL BE GOVERNED BY AND ITS
PROVISIONS CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE, AS
APPLIED TO CONTRACTS BETWEEN DELAWARE RESIDENTS ENTERED INTO AND TO BE PERFORMED
ENTIRELY WITHIN DELAWARE.



                            [Signature page follows.]



                                       7
<PAGE>


         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the Effective Date.

                                                COMPANY:
                                                Cyberonics, Inc.

                                                By: /s/ Robert P. Cummins
                                                    ---------------------
                                                     Chief Executive Officer


                                                DIRECTOR:

                                                /s/ Thomas A. Duerden, Ph.D.
                                                ----------------------------
                                                Thomas A. Duerden, Ph.D.


                                       8