UNITED STATES
                        SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549



                                  SCHEDULE 13G

                   UNDER THE SECURITIES EXCHANGE ACT OF 1934
                              (AMENDMENT NO. 6)*


                             Core Laboratories N.V.
--------------------------------------------------------------------------------
                                (Name of Issuer)

                                 Common Stock
--------------------------------------------------------------------------------
                        (Title of Class of Securities)


                                 N22717-10-7
            --------------------------------------------------------
                                (CUSIP Number)


                               December 31, 2003
--------------------------------------------------------------------------------
            (Date of Event Which Requires Filing of this Statement)


Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

   /X/       Rule 13d-1(b)
   / /       Rule 13d-1(c)
   / /       Rule 13d-1(d)


*The remainder of this cover page shall be filled out for a reporting
person's initial filing on this form with respect to the subject class of
securities, and for any subsequent amendment containing information which
would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise subject to the liabilities of that section
of the Act but shall be subject to all other provisions of the Act (however,
see the Notes).


                                      Page 1
                                    of 10 Pages



                                     SCHEDULE 13G

CUSIP NO. N22717-10-7                                        Page 2 of 10 Pages


-------------------------------------------------------------------------------
 (1) NAMES OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

     Citigroup Global Markets Inc.
     f/k/a "Salomon Smith Barney Inc."
-------------------------------------------------------------------------------
 (2) CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                       (a)  / /
                                                                       (b)  / /
-------------------------------------------------------------------------------
 (3) SEC USE ONLY



-------------------------------------------------------------------------------
 (4) CITIZENSHIP OR PLACE OF ORGANIZATION                              New York



-------------------------------------------------------------------------------
       NUMBER OF           (5) SOLE VOTING POWER                              0

        SHARES
                           ----------------------------------------------------
     BENEFICIALLY          (6) SHARED VOTING POWER                   4,421,718*

       OWNED BY
                           ----------------------------------------------------
        EACH               (7) SOLE DISPOSITIVE POWER                         0

      REPORTING
                           ----------------------------------------------------
       PERSON              (8) SHARED DISPOSITIVE POWER              4,421,718*

        WITH:
-------------------------------------------------------------------------------
(9) AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON     4,421,718*




-------------------------------------------------------------------------------
(10) CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES (SEE
     INSTRUCTIONS)  / /


-------------------------------------------------------------------------------
(11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)                   15.7%*



-------------------------------------------------------------------------------
(12) TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)                             BD


-------------------------------------------------------------------------------
* Includes shares for which the reporting person disclaims beneficial
  ownership.  See Item 4(a).



                                     SCHEDULE 13G

CUSIP NO. N22717-10-7                                       Page 3 of 10 Pages


-------------------------------------------------------------------------------
 (1) NAMES OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

     Citigroup Financial Products Inc.
     f/k/a "Salomon Brothers Holding Company Inc"
-------------------------------------------------------------------------------
 (2) CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                       (a)  / /
                                                                       (b)  / /
-------------------------------------------------------------------------------
 (3) SEC USE ONLY



-------------------------------------------------------------------------------
 (4) CITIZENSHIP OR PLACE OF ORGANIZATION                              Delaware



-------------------------------------------------------------------------------
       NUMBER OF           (5) SOLE VOTING POWER                              0

        SHARES
                           ----------------------------------------------------
     BENEFICIALLY          (6) SHARED VOTING POWER                   4,421,718*

       OWNED BY
                           ----------------------------------------------------
        EACH               (7) SOLE DISPOSITIVE POWER                         0

      REPORTING
                           ----------------------------------------------------
       PERSON              (8) SHARED DISPOSITIVE POWER              4,421,718*

        WITH:
-------------------------------------------------------------------------------
(9) AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON     4,421,718*




-------------------------------------------------------------------------------
(10) CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES (SEE
     INSTRUCTIONS)  / /


-------------------------------------------------------------------------------
(11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)                   15.7%*



-------------------------------------------------------------------------------
(12) TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)                             CO


-------------------------------------------------------------------------------
* Includes shares for which the reporting person disclaims beneficial
  ownership.  See Item 4(a).



CUSIP NO. N22717-10-7                                         Page 4 of 10 Pages


-------------------------------------------------------------------------------
 (1) NAMES OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

     Smith Barney Fund Management LLC
-------------------------------------------------------------------------------
 (2) CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                       (a)  / /
                                                                       (b)  / /
-------------------------------------------------------------------------------
 (3) SEC USE ONLY



-------------------------------------------------------------------------------
 (4) CITIZENSHIP OR PLACE OF ORGANIZATION                              Deleware



-------------------------------------------------------------------------------
       NUMBER OF           (5) SOLE VOTING POWER                              0

        SHARES
                           ----------------------------------------------------
     BENEFICIALLY          (6) SHARED VOTING POWER                   1,683,500*

       OWNED BY
                           ----------------------------------------------------
        EACH               (7) SOLE DISPOSITIVE POWER                         0

      REPORTING
                           ----------------------------------------------------
       PERSON              (8) SHARED DISPOSITIVE POWER              1,683,500*

        WITH:
-------------------------------------------------------------------------------
(9) AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON     1,683,500*




-------------------------------------------------------------------------------
(10) CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES (SEE
     INSTRUCTIONS)  / /


-------------------------------------------------------------------------------
(11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)                    6.0%*



-------------------------------------------------------------------------------
(12) TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)                             IA


-------------------------------------------------------------------------------
* Includes shares for which the reporting person disclaims beneficial
  ownership.  See Item 4(a).



                                     SCHEDULE 13G

CUSIP NO. N22717-10-7                                         Page 5 of 10 Pages


-------------------------------------------------------------------------------
 (1) NAMES OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

     Citigroup Global Markets Holdings Inc.
     f/k/a "Salomon Smith Barney Holdings Inc."
-------------------------------------------------------------------------------
 (2) CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                       (a)  / /
                                                                       (b)  / /
-------------------------------------------------------------------------------
 (3) SEC USE ONLY



-------------------------------------------------------------------------------
 (4) CITIZENSHIP OR PLACE OF ORGANIZATION                              New York



-------------------------------------------------------------------------------
       NUMBER OF           (5) SOLE VOTING POWER                              0

        SHARES
                           ----------------------------------------------------
     BENEFICIALLY          (6) SHARED VOTING POWER                   6,105,218*

       OWNED BY
                           ----------------------------------------------------
        EACH               (7) SOLE DISPOSITIVE POWER                         0

      REPORTING
                           ----------------------------------------------------
       PERSON              (8) SHARED DISPOSITIVE POWER              6,105,218*

        WITH:
-------------------------------------------------------------------------------
(9) AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON     6,105,218*




-------------------------------------------------------------------------------
(10) CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES (SEE
     INSTRUCTIONS)  / /


-------------------------------------------------------------------------------
(11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)                   21.7%*



-------------------------------------------------------------------------------
(12) TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)                             HC


-------------------------------------------------------------------------------
* Includes shares for which the reporting person disclaims beneficial
  ownership.  See Item 4(a).



                                     SCHEDULE 13G

CUSIP NO. N22717-10-7                                         Page 6 of 10 Pages


-------------------------------------------------------------------------------
 (1) NAMES OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

     Citigroup Inc.
-------------------------------------------------------------------------------
 (2) CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                       (a)  / /
                                                                       (b)  / /
-------------------------------------------------------------------------------
 (3) SEC USE ONLY



-------------------------------------------------------------------------------
 (4) CITIZENSHIP OR PLACE OF ORGANIZATION                              Delaware



-------------------------------------------------------------------------------
       NUMBER OF           (5) SOLE VOTING POWER                              0

        SHARES
                           ----------------------------------------------------
     BENEFICIALLY          (6) SHARED VOTING POWER                   6,200,905*
                                                                             **
       OWNED BY
                           ----------------------------------------------------
        EACH               (7) SOLE DISPOSITIVE POWER                         0

      REPORTING
                           ----------------------------------------------------
       PERSON              (8) SHARED DISPOSITIVE POWER              6,200,905*
                                                                             **

        WITH:
-------------------------------------------------------------------------------
(9) AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON     6,200,905*
                                                                             **

-------------------------------------------------------------------------------
(10) CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES (SEE
     INSTRUCTIONS)  / /


-------------------------------------------------------------------------------
(11) PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)                   22.0%*
                                                                             **

-------------------------------------------------------------------------------
(12) TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)                             HC



-------------------------------------------------------------------------------
*  Includes shares for which the reporting person disclaims beneficial
   ownership.  See Item 4(a).
** Includes shares held by the other reporting persons.



Item 1(a).   Name of Issuer:

             Core Laboratories N.V.

Item 1(b).   Address of Issuer's Principal Executive Offices:

             Herengracht 424
             1017 BZ Amsterdam
             The Netherlands

Item 2(a).   Name of Person Filing:

             Citigroup Global Markets Inc. ("CGM")
             Citigroup Financial Products Inc. ("CFP")
             Smith Barney Fund Management LLC ("SB Fund")
             Citigroup Global Markets Holdings Inc. ("CGM Holdings")
             Citigroup Inc. ("Citigroup")

Item 2(b).   Address or Principal Office or, if none, Residence:

             The address of the principal office of each of
             CGM, CFP and CGM Holdings is:

             388 Greenwich Street
             New York, NY 10013

             The address of the principal officer of SB fund is:

             333 West 34th Street
             New York, NY 10001

             The address of the principal office of Citigroup is:

             399 Park Avenue
             New York, NY 10043

Item 2(c).   Citizenship or Place of Organization:

             CGM and CGM Holdings are New York corporations.

             SB Fund is a Delaware limited liability company.

             CFP and Citigroup are Delaware corporations.

Item 2(d).   Title of Class of Securities:

             Common Stock

Item 2(e).   Cusip Number:

             N22717-10-7



                                       Page 7
                                     of 10 Pages


Item 3.      If this Statement is Filed Pursuant to Sections 240.13d-1(b) or
             240.13d-2(b) or (c), Check Whether the Person Filing is a(n):

             (a)  [X] Broker or dealer registered under section 15 of the
                      Act (15 U.S.C. 78o);

             (b)  [ ] Bank as defined in section 3(a)(6) of the Act
                      (15 U.S.C. 78c);

             (c)  [ ] Insurance company as defined in section 3(a)(19) of
                      the Act (15 U.S.C. 78c);

             (d)  [ ] Investment company registered under Section 8 of the
                      Investment Company Act of 1940 (15 U.S.C. 80a-8);

             (e)  [X] Investment adviser in accordance with Section
                      240.13d-1(b)(1)(ii)(E);

             (f)  [ ] Employee benefit plan or endowment fund in accordance
                      with Section 240.13d-1(b)(1)(ii)(F);

             (g)  [X] Parent holding company or control person in accordance
                      with Section  240.13d-1(b)(1)(ii)(G);

             (h)  [ ] Savings association as defined in Section 3(b) of the
                      Federal Deposit Insurance Act (12 U.S.C. 1813);

             (i)  [ ] Church plan that is excluded from the definition of an
                      investment company under Section 3(c)(14) of the
                      Investment Company Act of 1940 (15 U.S.C. 80a-3)

             (j)  [ ] Group, in accordance with Section 240.13d-1(b)(1)(ii)(J).


Item 4.   Ownership. (as of December 31, 2003)

          (a)  Amount beneficially owned: See item 9 of cover pages

              (Includes shares for which the reporting person disclaims
              beneficial ownership.)

          (b)  Percent of Class: See item 11 of cover pages

          (c)  Number of shares as to which the person has:

                  (i)   sole power to vote or to direct the vote:

                  (ii)  shared power to vote or to direct the vote:

                  (iii) sole power to dispose or to direct the disposition of:

                  (iv)  shared power to dispose or to direct the disposition of:


         See Items 5-8 of cover pages


                                       Page 8
                                     of 10 Pages


Item 5.   Ownership of Five Percent or Less of a Class.

          If this statement is being filed to report the fact that as of the
          date hereof the reporting person has ceased to be the beneficial owner
          of more than five percent of the class of securities, check the
          following [  ].

Item 6.   Ownership of More Than Five Percent on Behalf of Another Person.

          Not Applicable.

Item 7.   Identification and Classification of the Subsidiary which Acquired
          the Security being Reported on by the Parent Holding Company.

          CFP is the sole stockholder of CGM. CGM Holdings is the sole
          stockholder of CFP and the sole member of SB Fund. Citigroup is the
          sole stockholder of CGM Holdings.

Item 8.   Identification and Classification of Members of the Group.

          Not Applicable.

Item 9.   Notice of Dissolution of Group.

          Not Applicable.



                                       Page 9
                                     of 10 Pages



Item 10.  Certification.

          By signing below I certify that, to the best of my knowledge and
belief, the securities referred to above were acquired and are held in the
ordinary course of business and were not acquired and are not held for the
purpose of or with the effect of changing or influencing the control of the
issuer of the securities and were not acquired and are not held in connection
with or as a participant in any transaction having that purpose or effect.

SIGNATURE.

          After reasonable inquiry and to the best of my knowledge and
belief, I certify that the information set forth in this statement is true,
complete and correct.

Dated:  February 10, 2004


                     CITIGROUP GLOBAL MARKETS INC.


                     By: /s/ Serena D. Moe
                         --------------------------------------------
                         Name:  Serena D. Moe
                         Title: Assistant Secretary



                     CITIGROUP FINANCIAL PRODUCTS INC.


                     By: /s/ Serena D. Moe
                         --------------------------------------------
                         Name:  Serena D. Moe
                         Title: Assistant Secretary



                     SMITH BARNEY FUND MANAGEMENT LLC


                     By: /s/ Thomas C. Mandia
                         --------------------------------------------
                         Name:  Thomas C. Mandia
                         Title: Secretary



                     CITIGROUP GLOBAL MARKETS HOLDINGS INC.


                     By: /s/ Serena D. Moe
                         --------------------------------------------
                         Name:  Serena D. Moe
                         Title: Assistant Secretary



                     CITIGROUP INC.


                     By: /s/ Serena D. Moe
                         --------------------------------------------
                         Name:  Serena D. Moe
                         Title: Assistant Secretary



                                 Page 10
                               of 10 Pages



                          EXHIBIT INDEX TO SCHEDULE 13G
                          -----------------------------



EXHIBIT 1
---------

Agreement among CGM, CFP, SB Fund, CGM Holdings and Citigroup as to joint
filing of Schedule 13G