REGISTRATION RIGHTS AGREEMENT

         This Registration Rights Agreement (the "Rights Agreement") is entered
into as of December 16, 1997 by and among G.S. Beckwith Gilbert (the
"Shareholder") and Transgenomic, Inc. (the "Company").

         Section 1. DEFINITIONS. Certain other terms utilized in this Agreement
shall have the meanings indicated herein:

         "COMMISSION" means the U.S. Securities and Exchange Commission.

         "EXCHANGE ACT" means the Securities Exchange Act of 1934, as amended.

         "REGISTRABLE SECURITIES" shall consist of the shares of Common Stock
acquired by the Shareholder pursuant to the warrants issued by the Company to
the Shareholder pursuant to the terms of a Securities Purchase Agreement by and
between the Shareholder and the Company and dated as of the date hereof.
Registrable Securities shall not include: (i) any of such shares sold pursuant
to an effective registration statement under the Securities Act; (ii) any of
such shares sold under circumstances in which all of the applicable conditions
to Rule 144 (or successor provision) under the Securities Act are met; and (iii)
any of such shares that are no longer subject to any restrictions on transfer
pursuant to Rule 144(k) (or successor provision) under the Securities Act.

         "REGISTRATION EXPENSES" means all expenses incurred by the Company in
connection with the registration of Registrable Securities pursuant to this
Agreement, including (a) all registration and filing fees paid to the
Commission; (b) fees and expenses of compliance with state securities or blue
sky laws (including reasonable fees and disbursements of counsel in connection
with blue sky qualifications of the Registrable Securities); (c) printing
expenses; (d) internal expenses (including, without limitation, all salaries and
expenses of the Company's officers and employees performing legal or accounting
duties); (e) the fees and expenses incurred in connection with any listing of
the Registrable Securities on a national or regional exchange, the NASDAQ Stock
Market or similar facility; (f) fees and expenses of counsel for the Company and
fees and expenses for independent certified public accountants retained by the
Company (including the expenses of any comfort letters or costs associated with
the delivery by any independent certified public accountants of any comfort
letters); and (g) the reasonable fees and expenses of any special experts
retained by the Company in connection with such registration.

         "SECURITIES ACT" means the Securities Act of 1933, as amended.

         "SELLING EXPENSES" means all underwriting fees, discounts, commissions
or expenses attributable to any sale of all or part of the Registrable
Securities.

         Section 2. REGISTRATION RIGHTS. (a) If the Company proposes to file a
registration statement under the Securities Act with respect to either a primary
or secondary offering by the Company of equity securities for its own account
(other than a registration statement relating solely to (i) securities to be
offered to employees pursuant to a stock option, stock savings, or


<PAGE>


other employee benefit plan of the Company or its affiliates; (ii) securities
proposed to be issued in exchange for securities or assets of, or in connection
with a merger or consolidation with, another corporation; (iii) securities to be
offered by the Company generally to any class or series of its then-existing
security holders; or (iv) securities to be offered or issued pursuant to a
combination of the foregoing transactions), then the Company shall give written
notice of such proposed filing to the Shareholder as soon as practicable (but in
no event less than 30 days before the anticipated filing date of such
registration statement), and such notice shall offer the opportunity to include
all or any part of the Registerable Shares owned by the Shareholder with the
securities of the Company being so registered. The Shareholder shall have 15
days following receipt of such notice to request in writing inclusion of all or
any portion of his Registerable Shares in such registration, which request shall
specify the number of Registerable Shares the Shareholder proposes to sell
pursuant thereto.

         (b) Whenever the Shareholder requests that all or part of his
Registerable Shares be included in a proposed registration, the Company shall
use its reasonable best efforts to effect the registration of such Registerable
Shares and to cause the managing underwriter of any proposed underwritten
offering to permit the requested Registerable Shares to be included in such
registration on the same terms and conditions as any similar securities included
therein. The Shareholder may only participate in an underwritten registration
hereunder if he (i) agrees to sell his Registerable Shares on the basis provided
in any underwriting arrangements and (ii) completes and executes all
questionnaires, powers of attorney, indemnities, underwriting agreements and
other documents reasonably required under the terms of such underwriting
arrangements and these registration rights. Among other things, the Shareholder
agrees, whether or not his Registerable Shares are included in an underwritten
offering, that he will join in any general agreement with the managing
underwriter not to effect any public sale or distribution of his Registerable
Shares, including a sale pursuant to Rule 144 under the Securities Act, for a
period of time not to exceed 360 days.

         (c) Notwithstanding anything else set forth in this Section 2, the
Company may, at the discretion of a majority of its Board of Directors and
without the consent of the Shareholder, withdraw any registration and abandon
the proposed offering. Furthermore, if the managing underwriter of an
underwritten offering advises the Company that in its opinion either because of
(A) the size of the offering that the Company, the Shareholder or any other
shareholder desires to make or (B) the kind of securities that the Company and
the Shareholder intend to include in such offering, the success of the offering
could be materially and adversely affected by inclusion of the Registerable
Shares requested to be included, then

                  (i) in the event that the size of the offering is the basis of
         such managing underwriter's opinion, (x) the amount of equity
         securities being offered by any other shareholders of the Company
         pursuant to other registration rights agreements which the Company may
         be party to will be reduced to the extent necessary to reduce the total
         amount of shares included in such offering to the amount recommended by
         the managing underwriter and (y) if an additional reduction in the
         number of shares is required, then the amount of equity securities to
         be offered by the Company and the amount of Registerable Shares to be
         offered for the account of the Shareholder shall be proportionately
         reduced (on the basis of the number of shares each intended to include
         in such offering) to the extent


                                       2
<PAGE>


         necessary to reduce the total amount of shares included in such
         offering to the amount recommended by such managing underwriter; and

                  (ii) in the event that the kind or combination of securities
         to be offered is the basis of such managing underwriter's opinion, the
         amount of Registerable Shares to be included in such offering shall be
         reduced as described in clause (i) above or, if any such reduction
         would, in the judgment of the managing underwriter, be insufficient to
         substantially eliminate the adverse effect that inclusion of the
         Registerable Shares requested to be included could have on such
         offering, such Registerable Shares shall be excluded from such
         offering.

The Company agrees that it will not enter into any other registration rights
agreements which contradict or otherwise interfere with the operation of this
Section 2(c).

         (d) The registration rights under this Section 2 shall apply to the any
registration statement filed by the Company and declared effective under the
Securities Act, other than registration statements relating to those offerings
described in items (i) through (iv) of paragraph (a) of this Section 2.

         (e) The Company shall pay all Registration Expenses in connection with
the registration of Registerable Shares pursuant to this Section 2, whether or
not the registration statement becomes effective. The Shareholder shall pay all
Selling Expenses attributable to any sale of all or part of his Registerable
Shares in connection with any registration, whether or not the registration
statement becomes effective.

         (f) In connection with any registration required under this Agreement,
the Company shall take the actions set forth below.

                  (i) The Company shall notify the Shareholder of any stop order
         issued or threatened by the Commission and will take all reasonable
         actions required to prevent the entry of such stop order or to remove
         it if entered.

                  (ii) The Company shall comply with the provisions of the
         Securities Act with respect to the disposition of all securities
         covered by a registration statement filed pursuant to this Agreement
         with respect to the disposition of all Registrable Securities covered
         by such registration statement in accordance with the intended methods
         of disposition by the Shareholder as set forth in such registration
         statement.

                  (iii) The Company shall furnish to the Shareholder and each
         underwriter, if any, of Registrable Securities covered by a
         registration statement filed pursuant to this Agreement, such number of
         copies of such registration statement, each amendment and supplement
         thereto (in each case including all exhibits thereto), and the
         prospectus included in such registration statement (including each
         preliminary prospectus), in conformity with the requirements of the
         Securities Act, and such other documents as a Shareholder may
         reasonably request in order to facilitate the disposition of the
         Registrable Securities.

                  (iv) The Company shall use its commercially reasonable best
         efforts to register or qualify the Registrable Securities under the
         securities or "blue sky" laws of each state of


                                       3
<PAGE>


         the United States of America as the Shareholder or any of the
         underwriters, if any, of the Registrable Securities covered by a
         registration statement filed hereunder requests to the extent such
         request is deemed reasonable by the Board of Directors of the Company
         in its sole discretion, and shall do any and all other acts and things
         which may be reasonably necessary or advisable to enable the
         Shareholder and each underwriter, if any, to consummate the disposition
         in such states of the Registrable Securities; provided that the Company
         shall not be required to (A) qualify generally to do business in any
         jurisdiction where it would not otherwise be required to qualify but
         for this subsection (iv), (B) subject itself to taxation in any such
         jurisdiction or (C) consent to general service of process in any such
         jurisdiction.

                  (v) The Company shall immediately notify the Shareholder of
         the happening of any event which comes to the Company's attention if,
         as a result of such event, the prospectus included in the registration
         statement filed under this Agreement contains any untrue statement of a
         material fact or omits to state any material fact necessary to make the
         statements therein, in light of the circumstances under which they were
         made, not misleading, and the Company shall promptly prepare and
         furnish to the Shareholder and file with the Commission a supplement or
         amendment to such prospectus so that such prospectus will no longer
         contain any untrue statement of a material fact or omit to state any
         material fact necessary to make the statements therein, in light of the
         circumstances under which they were made, not misleading.

                  (vi) The Company shall make available for inspection by the
         Shareholder, any underwriter participating in any disposition pursuant
         to a registration statement filed under this Agreement, and any
         attorney, accountant or other agent retained by the Shareholder or such
         underwriters, all financial and other records, pertinent corporate
         documents and properties of the Company and its subsidiaries, as such
         person may reasonably request for the purpose of confirming that such
         registration statement does not contain any untrue statement of a
         material fact or omit to state any material fact necessary to make the
         statements therein, in light of the circumstances under which they were
         made, not misleading, provided that the Company obtains reasonably
         satisfactory assurances that such information will be used solely for
         such purpose and will be held in confidence (except to the extent that
         it is included in the registration statement). The Company shall cause
         the officers, directors and employees of the Company and each of its
         subsidiaries to supply such information and respond to such inquiries
         as the Shareholder or such underwriter may reasonably request or make
         for the purpose of confirming that such registration statement does not
         contain any untrue statement of a material fact or omit to state any
         material fact necessary to make the statements therein, in light of the
         circumstances under which they were made, not misleading, provided that
         the Company obtains reasonably satisfactory assurances that such
         information will be used solely for such purpose and will be held in
         confidence (except to the extent that it is included in the
         registration statement).

                  (vii) The Company shall use its commercially reasonable best
         efforts to obtain a "cold comfort" letter from the Company's
         independent public accountants in customary form and covering such
         matters of the type customarily covered by "cold comfort" letters as
         the Shareholder or the underwriters reasonably request.


                                       4
<PAGE>


                  (viii) The Company shall otherwise use its best commercially
         reasonable best efforts to comply with all applicable rules and
         regulations of the Commission, and make generally available to its
         security holders, as soon as reasonably practicable, an earnings
         statement covering a period (which may begin with the first fiscal
         quarter ending after the effective date of the registration statement)
         of at least 12 months after the effective date of the registration
         statement (as the term "effective date" is defined in Rule 158(c) under
         the Securities Act), which earnings statement shall satisfy the
         provisions of Section 11(a) of the Securities Act and Rule 158
         thereunder.

         Section 3. OTHER REGISTRATION RIGHTS. The Shareholder acknowledges that
certain other stockholders of the Company may now or hereafter have registration
rights, and that such other stockholders may be entitled to sell their
securities at the same time, or pursuant to the same registration and
underwriting, as the Holders hereunder.

         Section 4.  INDEMNIFICATION.

                  (a) INDEMNIFICATION BY THE COMPANY. The Company shall
         indemnify and hold harmless the Shareholder and each person, if any,
         who controls the Shareholder within the meaning of Section 15 of the
         Securities Act or Section 20 of the Exchange Act from and against any
         and all losses, claims, damages, liabilities and expenses (including
         reasonable costs of investigation) arising out of or based upon any
         untrue statement or alleged untrue statement of a material fact
         contained in any registration statement or prospectus relating to the
         Registrable Securities or in any amendment or supplement thereto or in
         any preliminary prospectus, or arising out of or based upon any
         omission or alleged omission to state therein a material fact required
         to be stated therein or necessary to make the statements therein not
         misleading, except insofar as such losses, claims, damages, liabilities
         or expenses arise out of, or are based upon, any such untrue statement
         or omission or allegation thereof contained in information furnished in
         writing to the Company by such Shareholder or on such Shareholder's
         behalf; and provided, further, that with respect to any untrue
         statement or omission or alleged untrue statement or omission made in
         any preliminary prospectus, the indemnity contained in this paragraph
         shall not apply to the extent that any such loss, claim, damage,
         liability or expense results from the fact that a current copy of the
         prospectus was not sent or given to the persons or entities asserting
         any such loss, claim, damage, liability or expense at or prior to the
         written confirmation of the sale of the Registrable Securities
         concerned to such persons or entities with a current copy of the
         prospectus and such current copy of the prospectus would have cured the
         defect giving rise to such loss, claim, damage, liability or expense.

                  (b) INDEMNIFICATION BY SHAREHOLDER. The Shareholder agrees to
         indemnify and hold harmless the Company and each person, if any, who
         controls the Company within the meaning of either Section 15 of the
         Securities Act or Section 20 of the Exchange Act to the same extent as
         the foregoing indemnity from the Company to the Shareholder, but only
         with respect to information furnished in writing by the Shareholder or
         on his behalf. The Shareholder agrees to indemnify and hold harmless
         the underwriters of the Registrable Securities, their officers and
         directors and each person who controls such underwriters on terms
         consistent with industry standards in effect at such time.


                                       5
<PAGE>


         Section 5.          MISCELLANEOUS.

                  (a) NOTICES. All notices that are required or may be given
         pursuant to the terms of this Agreement shall be in writing and shall
         be sufficient in all respects if given in writing and delivered
         personally or by a recognized courier service or by registered or
         certified mail, postage prepaid, to any party at its address set forth
         below, with a copy of same by any of the authorized means to the
         indicated person or persons:

         If to the Company: Transgenomic, Inc.
                                    5600 South 42nd Street
                                    Omaha, Nebraska  68107
                                    Attention:  P. Thomas Pogge, General Counsel

         If to Shareholder: G.S. Beckwith Gilbert
                                    Field Point Capital Management Company
                                    104 Field Point Road
                                    Greenwich, Connecticut 06830

                  Any notice or other communication shall be deemed to have been
         given on the day it is personally delivered or delivered by a
         recognized courier service as aforesaid or, if mailed, on the third day
         after it is mailed. Any party may change its address for notices or the
         person or persons authorized to receive notices for it by providing
         notice to the other parties in accordance with this Section.

                  (b) INVALIDITY OF PROVISIONS. If any provision of this
         Agreement is determined to be invalid, illegal or unenforceable, in
         whole or in part, then the parties shall be relieved of all obligations
         arising under such provision to the extent it is invalid, illegal or
         unenforceable, and such provision shall be reformed to the extent
         necessary to make it legal and enforceable while preserving its intent
         or, if that is not possible, by substituting therefor another provision
         that is legal and enforceable and achieves the same objectives.

                  (c) SECTION TITLES. All section titles and captions in this
         Agreement are for convenience only, shall not be deemed part of this
         Agreement and in no way shall define, limit, extend or describe the
         scope or intent of any provisions of this Agreement.

                  (d) FURTHER ACTS. The parties shall execute all documents,
         provide all information and take all such actions as may be reasonably
         necessary or appropriate to achieve the purposes of this Agreement and
         to accomplish the transactions contemplated hereby.

                  (e) ENTIRE AGREEMENT; WAIVER. This Agreement constitutes the
         entire agreement among the parties hereto pertaining to the subject
         matter hereof and supersedes all prior agreements and understandings
         relating to the subject matter hereof. This Agreement cannot be
         modified or amended except in writing signed by the party against whom
         enforcement is sought. No waiver by a party of any of the provisions of
         this Agreement shall be deemed or shall constitute a waiver of any
         other provision of this Agreement, nor shall any such waiver constitute
         a continuing waiver.


                                       6
<PAGE>


                  Although the Shareholder will become a party to the
         Shareholders Agreement, dated July 1, 1997, by and among the Company
         and its shareholders (the "Shareholders Agreement") upon the exercise
         of his warrants, the registration rights granted pursuant to this
         Agreement shall supersede any such rights stated in Section 8 of the
         Shareholders Agreement with respect to the Registerable Shares (but not
         with respect to any other shares of the Company's equity securities
         acquired or held by the Shareholder).

                  (f) COUNTERPARTS. This Agreement may be executed in multiple
         counterparts, all of which together shall constitute one agreement
         binding on the parties hereto, notwithstanding that the parties are not
         signatories to the same counterpart.

                  (g) GOVERNING LAW. This Agreement shall be governed by and
         construed in accordance with the substantive laws of the State of
         Nebraska and the United States, as applicable, without giving effect to
         any conflict of laws provisions that might result in the application of
         the laws of another jurisdiction.

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed as of date first above written.

         TRANSGENOMIC, INC.

         By /s/ Collin D'Silva
            --------------------------------
         Its Chief Executive Officer
            --------------------------------




         /s/ G.S. Beckwith Gilbert
            --------------------------------
         G.S. Beckwith Gilbert

                                       7

Source: OneCLE Business Contracts.