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                                                                  EXHIBIT 10.20

                             CORE LABORATORIES N.V.
                          1995 LONG-TERM INCENTIVE PLAN
             (AS AMENDED AND RESTATED EFFECTIVE AS OF MAY 29, 1997)

                            EXECUTIVE SHARE MATCHING
                           RESTRICTED SHARE AGREEMENT
             (AS AMENDED AND RESTATED EFFECTIVE AS OF JUNE 1, 2002)



         THIS AGREEMENT (this "Agreement") is made as of this first day of
March, 2003, between Core Laboratories N.V., a Dutch limited liability company
(the "Company"), and David Demshur ("Participant").

                                    RECITALS:

         WHEREAS, the Company has heretofore adopted the Core Laboratories N.V.
1995 Long-Term Incentive Plan (as amended and restated effective as of May 29,
1997) (the "Plan") for the purposes of retaining and rewarding select employees
of the Company and its subsidiaries; and

         WHEREAS, to carry out the purposes of the Plan, the Company and
Participant have heretofore entered into an Executive Share Matching Restricted
Share Agreement dated June 1, 2002 (the "Original Agreement") pursuant to which
the Company was to issue Participant shares of common stock of the Company,
which shares would be subject to certain restrictions; and

         WHEREAS, said shares have not yet been issued under the Original
Agreement, and, effective as of June 1, 2002 (the effective date of the Original
Agreement), the Company and Participant desire to amend and restate the Original
Agreement in its entirety to reflect certain changes to the initial arrangement
that have been agreed to by the Company and Participant;

         NOW, THEREFORE, in consideration of the mutual agreements and other
matters set forth herein and in the Plan, the Company and Participant agree that
the Original Agreement shall be and hereby is restated in its entirety into this
Agreement, and the Company and Participant further agree as follows:

                                   AGREEMENTS:

                                       I.
                                   DEFINITIONS

         1.1 DEFINITIONS. Wherever used in this Agreement, the following words
and phrases when capitalized will have the meanings ascribed below, unless the
context clearly indicates to the contrary, and all other capitalized terms used
in this Agreement, which are not defined below, will have the meanings set forth
in the Plan.

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         (1)  "AGREEMENT" means this Executive Share Matching Restricted Share
              Agreement (as Amended and Restated Effective as of June 1, 2002)
              between Participant and the Company.

         (2)  "CAUSE" means a determination by the Committee that Participant
              has been convicted of, or plead nolo contendere to, any crime
              involving moral turpitude or a felony.

         (3)  "DATE OF GRANT" means June 1, 2002.

         (4)  "DISABILITY" means a determination by the Committee, based on a
              written medical opinion (unless waived by the Committee as
              unnecessary), that Participant is permanently incapable of
              continuing his usual and customary employment with the Company or
              any Subsidiary for physical or mental reasons.

         (5)  "FORFEITURE RESTRICTIONS" means the Forfeiture Restrictions as set
              forth in Section 4.1 herein.

         (6)  "GROSS-UP FORFEITURE FRACTION" means a fraction, the numerator of
              which is the number of Gross-Up Qualifying Shares with respect to
              which Participant does not maintain continuous ownership
              throughout the Tax Gross-Up Period, and the denominator of which
              equals the number of Gross-Up Qualifying Shares.

         (7)  "GROSS-UP FORFEITURE RESTRICTIONS" means the Gross-Up Forfeiture
              Restrictions as set forth in Section 6.3(b) herein.

         (8)  "GROSS-UP QUALIFYING SHARES" means the sum of (i) the number of
              Qualifying Shares with respect to which Participant has maintained
              continuous ownership from the Date of Grant through the date
              Restricted Matching Shares become Vested pursuant to Section 5.1,
              plus (ii) the product of (x) the number of Restricted Matching
              Shares that become Vested pursuant to Section 5.1 multiplied by
              (y) 100% minus the Tax Rate as of the date of such Vesting.
              Notwithstanding the foregoing, the Committee, in its sole
              discretion, may adjust (upwards or downwards) the Tax Rate to
              reflect Participant's actual tax liabilities with respect to the
              lapse of the Forfeiture Restrictions with respect to the
              Restricted Matching Shares, and Participant shall provide such
              information as the Committee may request for purposes of
              determining whether to adjust the Tax Rate.

         (9)  "INVOLUNTARY TERMINATION" means a termination of Participant's
              Service that (i) is not initiated in whole or in part by
              Participant, (ii) is not a termination as a result of Disability
              or death, and (iii) is not consented to by Participant.

         (10) "NORMAL RETIREMENT DATE" means the date Participant attains the
              age of 60 and completes 10 years of Service.

         (11) "PARTICIPANT" means the individual to whom the Restricted Matching
              Shares are granted as specified above.

         (12) "PARTICIPANT'S SPOUSE" means the individual, if any, who is the
              spouse of Participant on the Date of Grant.


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         (13) "QUALIFYING SHARES" means (i) Common Shares purchased and held by
              Participant in open market transactions on or before the Date of
              Grant, excluding (A) "leveraged buy-out" Common Shares acquired in
              connection with the purchase of Core Laboratories from Western
              Atlas International, Inc., and excluding (B) Common Shares
              received in connection with the purchase or acquisition of a
              business by the Company or a Subsidiary; (ii) Common Shares
              acquired in open market purchases and held in Participant's
              account under the Core Laboratories Profit Sharing and Retirement
              Plan or its equivalent on or before the Date of Grant; (iii)
              Common Shares designated to be held in Participant's account under
              the Core Laboratories Deferred Compensation Plan or its equivalent
              on or before the Date of Grant; (iv) Common Shares acquired and
              held in Participant's individual retirement account or its
              equivalent on or before the Date of Grant; (v) Common Shares
              acquired and held in a family trust controlled by Participant or a
              family partnership controlled by Participant on or before the Date
              of Grant; and (vi) Common Shares acquired and held by
              Participant's Spouse in an account under a 401(k) plan, Keogh
              plan, individual retirement account, or other similar
              tax-qualified retirement savings plan on or before the Date of
              Grant.

         (14) "RESTRICTED GROSS-UP SHARES" means the Common Shares, if any,
              awarded in Participant's name pursuant to Section 6.3(a) and
              subject to the Gross-Up Forfeiture Restrictions.

         (15) "RESTRICTED MATCHING SHARES" means the Common Shares hereby issued
              in Participant's name pursuant to Section 2.1 and subject to the
              Forfeiture Restrictions.

         (16) "RESTRICTED QUALIFYING SHARES" means the Restricted Qualifying
              Shares as set forth in Section 3.1 herein.

         (17) "SERVICE" means Participant's status as an employee of the Company
              or a Subsidiary or a corporation or parent or subsidiary of such
              corporation assuming or substituting the Restricted Matching
              Shares or Restricted Gross-Up Shares, as applicable.

         (18) "TAX GROSS-UP PAYMENT" means the Tax Gross-Up Payment as set forth
              in Section 6.1 herein.

         (19) "TAX GROSS-UP PERIOD" means the period beginning on the date
              Restricted Matching Shares become Vested pursuant to Section 5.1
              and ending on the earlier of (i) the second anniversary of such
              date, (ii) the effective date of a Change in Control, or (iii) the
              date Participant's Service terminates (x) on or after Normal
              Retirement Date or (y) by reason of death, Disability, or
              Involuntary Termination for reasons other than Cause.

         (20) "TAX RATE" means the highest combined federal and state and local
              and foreign income, earnings, Medicare, and any other tax rates
              applicable to Participant on the date of determination, net of the
              reduction in federal income taxes which could be obtained by
              deduction of such state, local, and foreign taxes; provided,
              however, that the Committee, in its sole discretion, may adjust
              (upwards or downwards) the Tax Rate to more accurately reflect
              Participant's tax liabilities.

         (21) "VEST" means (i) with respect to the Restricted Matching Shares,
              the lapse of the Forfeiture Restrictions with respect to all or a
              portion of the Restricted Matching Shares,


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         and (ii) with respect to the Restricted Gross-Up Shares, the lapse of
         the Gross-Up Forfeiture Restrictions with respect to all or a portion
         of the Restricted Gross-Up Shares.

         1.2 NUMBER AND GENDER. Wherever appropriate herein, words used in the
singular will be considered to include the plural, and words used in the plural
will be considered to include the singular. The masculine gender, where
appearing herein, will be deemed to include the feminine gender where
appropriate.

         1.3 HEADINGS OF ARTICLES AND SECTIONS. The headings of Articles and
Sections herein are included solely for convenience. If there is any conflict
between such headings and the text of the Plan, the text will control. All
references to Articles, Sections, and Paragraphs are to this document unless
otherwise indicated.

                                       II.
                       AWARD OF RESTRICTED MATCHING SHARES

         2.1 AWARD OF RESTRICTED MATCHING SHARES. On or after the Date of Grant,
47,394 Common Shares shall be issued as hereinafter provided in Participant's
name subject to certain restrictions thereon (such shares shall be herein
referred to as the "Restricted Matching Shares"). The Restricted Matching Shares
shall be issued upon acceptance hereof by Participant and upon satisfaction of
the conditions of this Agreement and the Plan. Participant hereby accepts the
Restricted Matching Shares when issued and agrees with respect thereto to the
terms and conditions set forth in this Agreement and the Plan. Further,
Participant acknowledges and agrees that the rights and benefits provided for in
this Agreement are in full substitution for the rights and benefits provided to
Participant under the Original Agreement, and Participant shall no longer have
any rights or claims to the rights and benefits provided for in the Original
Agreement.

                                      III.
                OWNERSHIP AND CERTIFICATION OF QUALIFYING SHARES

         3.1 OWNERSHIP OF QUALIFYING SHARES. As a condition of this award of
Restricted Matching Shares, Participant hereby certifies that he owns, as of the
Date of Grant, a number of Qualifying Shares that is at least equal to the
number of Restricted Matching Shares set forth in Article II. The term
"Restricted Qualifying Shares" shall refer to the number of Qualifying Shares
owned by Participant on the Date of Grant that is equal to the number of
Restricted Matching Shares set forth in Article II. For purposes of this
Agreement and notwithstanding any other provision in this Agreement to the
contrary, Common Shares owned by Participant's Spouse shall be deemed to be
owned by Participant for as long as Participant's Spouse owns such Common
Shares, without regard to the marital status of Participant and Participant's
Spouse after the Date of Grant.

         3.2 CERTIFICATION OF OWNERSHIP. Participant agrees to periodically
submit a signed certification of his current ownership of Restricted Qualifying
Shares and Restricted Matching Shares, as the Committee may request from time to
time. Such certification shall include information deemed relevant by the
Committee, including, by way of example and not limitation, the number of
Restricted Qualifying Shares and/or Restricted Matching Shares owned, the
account in which such shares are deposited or held, and the dates of purchase or
acquisition.


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Participant also agrees to submit any supporting documentation that the
Committee may request from time to time to verify ownership of such shares.

                                       IV.
                             FORFEITURE RESTRICTIONS

         4.1 FORFEITURE RESTRICTIONS.

         (a) The Restricted Matching Shares may not be sold, assigned, pledged,
exchanged, hypothecated or otherwise transferred, encumbered or disposed of to
the extent then subject to the Forfeiture Restrictions (as hereinafter defined).
In the event of termination of Participant's Service, Participant shall, for no
consideration, forfeit to the Company all Restricted Matching Shares to the
extent then subject to the Forfeiture Restrictions. In addition, in the event
Participant ceases to maintain continuous ownership of the Restricted Qualifying
Shares, Participant shall, for no consideration, forfeit to the Company the
number of Restricted Matching Shares to the extent then subject to the
Forfeiture Restrictions that is in excess of the number of Qualifying Shares for
which Participant has maintained continuous ownership. The prohibition against
transfer and the obligation to forfeit and surrender Restricted Matching Shares
to the Company upon (i) termination of Service or (ii) failure to maintain
ownership of the Restricted Qualifying Shares are herein referred to as the
"Forfeiture Restrictions."

         (b) The Forfeiture Restrictions shall be binding upon and enforceable
against any transferee of Restricted Matching Shares. The prohibitions of this
Section 4.1 shall not apply to the transfer of Restricted Matching Shares
pursuant to a plan of reorganization of the Company, but the stock, securities
or other property received in exchange therefore shall also become subject to
the Forfeiture Restrictions and provisions governing the lapsing of such
Forfeiture Restrictions applicable to the original Restricted Matching Shares
for all purposes of this Agreement, and the certificate representing such stock,
securities or other property shall be legended to show such restrictions.

                                       V.
                                     VESTING

         5.1 VESTING/LAPSE OF FORFEITURE RESTRICTIONS.

         (a) Subject to Sections 5.2 and 5.3, the Restricted Matching Shares
shall Vest on the third anniversary of the Date of Grant provided that the
following requirements are satisfied: (i) Participant's Service has been
continuous from the Date of Grant through the third anniversary of the Date of
Grant, and (ii) Participant has maintained continuous ownership of the
Restricted Qualifying Shares from the Date of Grant through the third
anniversary of the Date of Grant.

         (b) To the extent that Participant maintains continuous ownership of
some, but not all, of the Restricted Qualifying Shares and has thus forfeited a
portion of the Restricted Matching Shares pursuant to Section 4.1, the Vesting
of the Restricted Matching Shares described in this Section 5.1 shall be with
respect to only the number of Restricted Matching Shares that is equal to the
number of Qualifying Shares which Participant has maintained continuous
ownership from the Date of Grant through the third anniversary of the Date of
Grant.


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         5.2 ACCELERATION OF VESTING.
             ------------------------

         (a) If Participant's Service terminates (i) on or after Normal
Retirement Date, or (ii) by reason of death, Disability, or Involuntary
Termination for reasons other than Cause, the number of Restricted Matching
Shares that is equal to the number of Qualifying Shares which Participant has
maintained continuous ownership from the Date of Grant through the effective
date of such termination of Participant's Service shall, as of the effective
date of such termination of Participant's Service, become Vested.

         (b) In the event of a Change in Control while Participant is in the
Service of the Company or a Subsidiary, the number of Restricted Matching
Shares that is equal to the number of Qualifying Shares which Participant has
maintained continuous ownership from the Date of Grant through the effective
date of such Change in Control shall, as of the effective date of such Change
in Control, become Vested.

         5.3 EFFECT OF TERMINATION OF SERVICE OR LACK OF CONTINUOUS OWNERSHIP ON
             -------------------------------------------------------------------
             VESTING.
             --------

         (a) Except as provided in Section 5.2, upon termination of
Participant's Service for any reason, the Restricted Matching Shares shall be
immediately forfeited to the extent not then Vested.

         (b) Upon Participant's failure to maintain continuous ownership of the
Restricted Qualifying Shares, the number of Restricted Matching Shares that is
in excess of the number of Qualifying Shares for which Participant has
maintained continuous ownership since the Date of Grant shall be immediately
forfeited to the extent not then Vested.

                                       VI.
                              TAX GROSS-UP PAYMENT
                              --------------------

         6.1 AMOUNT OF TAX GROSS-UP PAYMENT. On, or as soon as administratively
             -------------------------------
practicable after, the date, if any, upon which some or all of the Restricted
Matching Shares become Vested, the Company shall provide Participant with an
amount that is intended to reimburse Participant for tax liabilities resulting
from (i) the lapse of the Forfeiture Restrictions with respect to the Vested
Restricted Matching Shares and (ii) the payment of the Tax Gross-Up Payment
provided for in this Article. The payment described in the preceding sentence,
which shall be referred to as the "Tax Gross-Up Payment," shall be paid in cash
or Common Shares (as provided in Section 6.2 or Section 6.3, as applicable), and
the amount of the Tax Gross-Up Payment shall be equal to (A) the amount required
to be taken into gross income by Participant by reason of the lapse of the
Forfeiture Restrictions with respect to the Vested Restricted Matching Shares,
multiplied by (B) a fraction, the numerator of which is the Tax Rate as of the
date such shares become Vested, and the denominator of which is 100% minus the
Tax Rate as of the date such shares become Vested. Notwithstanding the
foregoing, the Committee, in its sole discretion, may adjust (upwards or
downwards) the amount determined pursuant to the preceding sentence to more
accurately reflect Participant's tax liabilities. Participant agrees to provide
such information as the Committee may request for purposes of determining
whether to adjust such amount.


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         6.2 PAYMENT OF TAX GROSS-UP PAYMENT IN CASH. If Restricted Matching
Shares become Vested pursuant to Section 5.2, then the Company shall pay the
Tax Gross-Up Payment to Participant (or to Participant's estate in the event of
the death of Participant) in a single, lump sum cash payment.

         6.3 PAYMENT OF TAX GROSS-UP PAYMENT IN COMMON SHARES.

         (a) If Restricted Matching Shares become Vested pursuant to Section
5.1, then the Company shall pay the Tax Gross-Up Payment to Participant in the
form of restricted Common Shares (the "Restricted Gross-Up Shares") awarded
under the Plan. The number of Restricted Gross-Up Shares to be so awarded shall
be equal to (i) the amount of the Tax Gross-Up Payment determined pursuant to
Section 6.1 divided by (ii) the Fair Market Value of a Common Share on the date
Restricted Matching Shares become Vested pursuant to Section 5.1. The Restricted
Gross-Up Shares shall be issued on, or soon as administratively practicable
after, the date Restricted Matching Shares become so Vested.

         (b) The Restricted Gross-Up Shares may not be sold, assigned, pledged,
exchanged, hypothecated or otherwise transferred, encumbered or disposed of to
the extent then subject to the Gross-Up Forfeiture Restrictions (as hereinafter
defined). In the event of termination of Participant's Service, Participant
shall, for no consideration, forfeit to the Company all Restricted Gross-Up
Shares to the extent then subject to the Gross-Up Forfeiture Restrictions. In
addition, in the event Participant ceases to maintain continuous ownership of
the Gross-Up Qualifying Shares, Participant shall, for no consideration, forfeit
to the Company the number of Restricted Gross-Up Shares to the extent then
subject to the Gross-Up Forfeiture Restrictions that is equal to the total
number of Restricted Gross-Up Shares multiplied by the Gross-Up Forfeiture
Fraction. The prohibition against transfer and the obligation to forfeit and
surrender Restricted Gross-Up Shares to the Company upon (i) termination of
Service or (ii) failure to maintain ownership of the Gross-Up Qualifying Shares
are herein referred to as the "Gross-Up Forfeiture Restrictions." The Gross-Up
Forfeiture Restrictions shall be binding upon and enforceable against any
transferee of Restricted Gross-Up Shares. The prohibitions of this Section
6.3(b) shall not apply to the transfer of Restricted Gross-Up Shares pursuant to
a plan of reorganization of the Company, but the stock, securities or other
property received in exchange therefore shall also become subject to the
Gross-Up Forfeiture Restrictions and provisions governing the lapsing of such
Gross-Up Forfeiture Restrictions applicable to the original Restricted Gross-Up
Shares for all purposes of this Agreement, and the certificates representing
such stock, securities or other property shall be legended to show such
restrictions

         (c) Subject to Sections 6.3(d) and 6.3(e), the Restricted Gross-Up
Shares shall Vest on the second anniversary of the date Restricted Matching
Shares became Vested pursuant to Section 5.1 provided that the following
requirements are satisfied: (i) Participant's Service has been continuous from
the date Restricted Matching Shares became so Vested through the second
anniversary of such date, and (ii) Participant has maintained continuous
ownership of the Gross-Up Qualifying Shares from the date Restricted Matching
Shares became so Vested through the second anniversary of such date. To the
extent that Participant maintains continuous ownership of some, but not all, of
the Gross-Up Qualifying Shares and has thus forfeited a portion of the
Restricted Gross-Up Shares pursuant to Section 6.3(b), the Vesting of the
Restricted Gross-Up Shares described in this Section 6.3(c) shall be with
respect to only a number of Restricted


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Gross-Up Shares equal to (x) the total number of Restricted Gross-Up Shares
multiplied by (y) one minus the Gross-Up Forfeiture Fraction.

         (d) If Participant's Service terminates (i) on or after Normal
Retirement Date, or (ii) by reason of death, Disability, or Involuntary
Termination for reasons other than Cause, then, as of the effective date of such
termination of Participant's Service, Participant shall become Vested with
respect to a number of Restricted Gross-Up Shares equal to (x) the total number
of Restricted Gross-Up Shares multiplied by (y) one minus the Gross-Up
Forfeiture Fraction. If a Change in Control occurs while Participant is in the
Service of the Company or a Subsidiary, then, as of the effective date of such
Change in Control, Participant shall become Vested with respect to a number of
Restricted Gross-Up Shares equal to (A) the total number of Restricted Gross-Up
Shares multiplied by (B) one minus the Gross-Up Forfeiture Fraction.

         (e) Except as provided in Section 6.3(d), upon termination of
Participant's Service for any reason, the Restricted Gross-Up Shares shall be
immediately forfeited to the extent not then Vested. Upon Participant's failure
to maintain continuous ownership of the Gross-Up Qualifying Shares, a number of
Restricted Gross-Up Shares shall be forfeited in an amount equal to (i) the
total number of Restricted Gross-Up Shares multiplied by (ii) the Gross-Up
Forfeiture Fraction.

                                      VII.
                STATUS OF RESTRICTED MATCHING SHARES, RESTRICTED
                        GROSS-UP SHARES AND RESTRICTIONS

         7.1 STATUS OF RESTRICTED MATCHING SHARES AND RESTRICTED GROSS-UP
SHARES. With respect to the status of the Restricted Matching Shares and
Restricted Gross-Up Shares, if any, at the time of execution of this Agreement
Participant understands and agrees to all of the following:

         (a) Participant agrees that the Restricted Matching Shares and the
Restricted Gross-Up Shares, if any, will not be sold or otherwise disposed of in
any manner that would constitute a violation of any applicable federal, state or
foreign securities laws.

         (b) Participant agrees that (i) the certificates representing the
Restricted Matching Shares and the Restricted Gross-Up Shares, if any, may bear
such legend or legends as the Committee deems appropriate in order to reflect
the Forfeiture Restrictions and Gross-Up Forfeiture Restrictions, as applicable,
and to ensure compliance with applicable securities laws, (ii) the Company may
refuse to register the transfer of the Restricted Matching Shares and/or the
Restricted Gross-Up Shares on the stock transfer records of the Company if such
proposed transfer would in the opinion of counsel satisfactory to the Company
constitute a violation of any applicable securities law or the Forfeiture
Restrictions or the Gross-Up Forfeiture Restrictions, as applicable, and (iii)
the Company may give related instructions to its transfer agent, if any, to stop
registration of the Restricted Matching Shares and/or the Restricted Gross-Up
Shares.

         7.2 CERTIFICATES AND SHAREHOLDER RIGHTS.

         (a) Restricted Matching Shares awarded pursuant to this Agreement will
be represented by a stock certificate registered in the name of Participant.
Participant will have the right to receive dividends with respect to Restricted
Matching Shares, to vote Restricted Matching Shares, and to enjoy all other
shareholder rights, except that (i) Participant will not be


                                       8

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entitled to delivery of the stock certificate until the Forfeiture Restrictions
have lapsed, (ii) the Company will retain custody of the Restricted Matching
Shares until the Forfeiture Restrictions have lapsed, (iii) Participant may not
sell, transfer, pledge, exchange, hypothecate, or otherwise dispose of the
Restricted Matching Shares until the Forfeiture Restrictions have lapsed, (iv) a
breach of the terms and conditions established by the Committee pursuant to this
Agreement will cause a forfeiture of the Restricted Matching Shares, and (v) any
additional Common Shares or other securities issued or transferred with respect
to the Restricted Matching Shares pursuant to a stock dividend, stock split,
recapitalization, combination of shares, merger, consolidation, separation or
reorganization or any other change in the capital structure of the Company shall
be subject to the same Forfeiture Restrictions on transfer as the Restricted
Matching Shares and shall become Restricted Matching Shares for purposes of this
Agreement. The Company, on the date of grant of the Restricted Matching Shares
or anytime thereafter, may require Participant to deliver to the Company a stock
power, endorsed in blank, relating to the Restricted Matching Shares. As soon as
practicable after the expiration of the Forfeiture Restrictions, the Company
shall deliver to Participant the stock certificates and any other property no
longer subject to the Forfeiture Restrictions.

         (b) Restricted Gross-Up Shares, if any, awarded pursuant to this
Agreement will be represented by a stock certificate registered in the name of
Participant. Participant will have the right to receive dividends with respect
to Restricted Gross-Up Shares, to vote Restricted Gross-Up Shares, and to enjoy
all other shareholder rights, except that (i) Participant will not be entitled
to delivery of the stock certificate until the Gross-Up Forfeiture Restrictions
have lapsed, (ii) the Company will retain custody of the Restricted Gross-Up
Shares until the Gross-Up Forfeiture Restrictions have lapsed, (iii) Participant
may not sell, transfer, pledge, exchange, hypothecate, or otherwise dispose of
the Restricted Gross-Up Shares until the Gross-Up Forfeiture Restrictions have
lapsed, (iv) a breach of the terms and conditions established by the Committee
pursuant to this Agreement will cause a forfeiture of the Restricted Gross-Up
Shares, and (v) any additional Common Shares or other securities issued or
transferred with respect to the Restricted Gross-Up Shares pursuant to a stock
dividend, stock split, recapitalization, combination of shares, merger,
consolidation, separation or reorganization or any other change in the capital
structure of the Company shall be subject to the same Gross-Up Forfeiture
Restrictions on transfer as the Restricted Gross-Up Shares and shall become
Restricted Gross-Up Shares for purposes of this Agreement. The Company, on the
date of grant of the Restricted Gross-Up Shares or anytime thereafter, may
require Participant to deliver to the Company a stock power, endorsed in blank,
relating to the Restricted Gross-Up Shares. As soon as practicable after the
expiration of the Gross-Up Forfeiture Restrictions, the Company shall deliver to
Participant the stock certificates and any other property no longer subject to
the Gross-Up Forfeiture Restrictions.

                                      VIII.
                                  MISCELLANEOUS

         8.1 CONTINUOUS OWNERSHIP OF COMMON SHARES. For purposes of this
Agreement, and notwithstanding any provision in this Agreement to the contrary,
Participant shall be deemed to have maintained continuous ownership of Common
Shares to the extent that such Common Shares are exchanged for other Common
Shares (including, by way of example and not limitation, a transaction in which
Common Shares are used to satisfy all or a portion of the exercise price of an
option to acquire additional Common Shares), but only to the extent that


                                       9

<PAGE>

Participant maintains (or is deemed to have maintained) continuous ownership of
the Common Shares received in such exchange or transaction. Notwithstanding the
foregoing, to the extent that the number of Common Shares received by
Participant is greater than the number of Common Shares given by Participant in
such exchange or transaction (including, by way of example and not limitation, a
transaction in which the number of Common Shares received as a result of the
exercise of an option is greater than the number of Common Shares used to
satisfy the exercise price), such excess number of Common Shares received by
Participant may be sold or otherwise disposed of without affecting the deemed
continuous ownership of the Common Shares that were given in such exchange or
transaction.

         8.2 SERVICE RELATIONSHIP. For purposes of this Agreement, any question
as to whether and when there has been a termination of Participant's Service,
and the cause of such termination, shall be determined by the Committee, and its
determination will be final.

         8.3 NOTICES. For purposes of this Agreement, notices and all other
communications provided for herein will be in writing and will be deemed to have
been duly given when personally delivered or (i) if Participant is outside of
the United States at the time of transmission of such notice, when sent by
courier, facsimile, or electronic mail, and (ii) if Participant is within the
United States at the time of transmission of such notice, when mailed by United
States registered or certified mail, return receipt requested, postage prepaid,
addressed to the Company at its principal executive office and to Participant at
the last address filed with the Company or to such other address as either party
may furnish to the other in writing in accordance herewith, except that notices
of changes of address will be effective only upon receipt.

         8.4 ELECTION UNDER SECTION 83(b) OF THE CODE. In connection with
receipt of the Restricted Matching Shares and/or the Restricted Gross-Up Shares,
if any, Participant understands that Participant should consult with
Participant's tax advisor regarding the advisability of filing with the Internal
Revenue Service an election under section 83(b) of the Code. As of the date of
this Agreement, (a) this election is optional and not required, (b) a separate
election would need to be filed with respect to Restricted Matching Shares and
with respect to Restricted Gross-Up Shares, (c) this election must be filed no
later than 30 days after the date on which Participant is granted the unvested
Restricted Matching Shares or the Restricted Gross-Up Shares, as applicable, (d)
the time period for making this election cannot be extended, and (e) the failure
to file an election under section 83(b) of the Code within the 30-day time
period will result in such election being unavailable to Participant.
Participant acknowledges (i) that Participant has been advised to consult with a
tax advisor now and at the time of receipt of any Restricted Matching Shares and
Restricted Gross-Up Shares regarding the tax consequences in connection with the
receipt of such shares and (ii) that timely filing of a section 83(b) election
is Participant's sole responsibility, even if Participant requests the Company
or its representative to file such election on Participant's behalf.

         8.5 RESTRICTIONS ON TRANSFER OF SHARES. No Restricted Matching Shares
or Restricted Gross-Up Shares may be sold, exchanged, transferred (including,
without limitation, any transfer to a nominee or agent of Participant),
assigned, pledged, hypothecated, or otherwise disposed of, including by
operation of law, in any manner that violates the Forfeiture Restrictions or
Gross-Up Forfeiture Restrictions, as applicable, and any other provisions of
this Agreement, and, until the date on which such restrictions lapse, any such
attempted disposition shall be void. The Company shall not be required (i) to
transfer on its books any shares that have been

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<PAGE>

transferred in violation of this Agreement or (ii) to treat as owner of such
shares, to accord the right to vote as such owner, or to pay dividends to any
transferee to whom such shares will have been so transferred.

         8.6 WITHHOLDING OF TAX. To the extent that the receipt of Restricted
Matching Shares, the lapse of any Forfeiture Restriction, the receipt of
Restricted Gross-Up Shares, the lapse of any Gross-Up Forfeiture Restriction, or
the receipt of a Tax Gross-Up Payment in cash results in compensation income or
wages to Participant for federal, state or local tax purposes, Participant shall
deliver to the Company at the time of such event such amount of money or Common
Shares as the Company may require to meet all obligations under applicable tax
laws or regulations, and, if Participant fails to do so, the Company is
authorized to withhold or cause to be withheld from any cash or Common Shares
remuneration then or thereafter payable to Participant any tax required to be
withheld by reason of such resulting compensation income or wages.

         8.7 NO EMPLOYMENT RIGHTS CONFERRED. No provision of this Agreement
shall confer any right upon Participant to continued employment with the Company
or any Subsidiary.

         8.8 LIMITATION OF RIGHTS. Any liability or obligation of the Company
with respect to a payment or future award under this Agreement shall be based
solely upon any contractual obligations that may be created by this Agreement,
and no such liability or obligation of the Company shall be deemed to be secured
by any pledge or other encumbrance on any property of the Company or a
Subsidiary.

         8.9 BINDING EFFECT. This Agreement shall be binding upon and inure to
the benefit of any successors to the Company and all persons lawfully claiming
under Participant.

         8.10 GOVERNING LAW. This Agreement shall be governed by, and construed
in accordance with, the laws of the state of Texas.

         IN WITNESS WHEREOF, the Company has caused this Agreement to be duly
executed by its officer thereunto duly authorized, and Participant has executed
this Agreement, as of the date first written above, all effective as of the Date
of Grant.

                                      CORE LABORATORIES N.V.,
                                      BY ITS SOLE MANAGING DIRECTOR,
                                      CORE LABORATORIES INTERNATIONAL B.V.


                                      By:
                                          -------------------------------------
                                          Name: Jacobus Schouten
                                          Title: Managing Director

                                      PARTICIPANT

                                      By:
                                          -------------------------------------
                                          Name: David Demshur


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