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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549



                                  SCHEDULE 13G


                    Under The Securities Exchange Act of 1934

                               (AMENDMENT NO.  4)*

                             Harvard BioScience Inc.
 -------------------------------------------------------------------------------
                                (Name of Issuer)


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


                                    416906105
 -------------------------------------------------------------------------------
                                 (CUSIP Number)


                                December 31, 2004
 -------------------------------------------------------------------------------
             (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 7 Pages






CUSIP No. 416906105                        13G                Page 2  of 7 Pages
------------






--------------------------------------------------------------------------------
1        NAME OF REPORTING PERSON
         S.S. OR I.R.S. IDENTIFICATION NO OF ABOVE PERSON
                          Kern Capital Management, LLC

                          13-3958232
--------------------------------------------------------------------------------

2         CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

                                                            (a)     / /

                                                            (b)     / /

--------------------------------------------------------------------------------
3         SEC USE ONLY


--------------------------------------------------------------------------------
4         CITIZENSHIP OR PLACE OF ORGANIZATION


                                    Delaware
--------------------------------------------------------------------------------

                             

                              5        SOLE VOTING POWER

                                       2,380,500
       NUMBER OF              --------------------------------------------------
  SHARES BENEFICIALLY         6        SHARED VOTING POWER
       OWNED BY         
         EACH                               -
       REPORTING              --------------------------------------------------
      PERSON WITH             7        SOLE DISPOSITIVE POWER

                                       2,380,500
                              --------------------------------------------------
                              8     SHARED DISPOSITIVE POWER

                                            -
--------------------------------------------------------------------------------
9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                                      2,380,500
--------------------------------------------------------------------------------
10       CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                        -
--------------------------------------------------------------------------------
11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                                      7.8%
--------------------------------------------------------------------------------
12       TYPE OF REPORTING PERSON*

                                       IA
--------------------------------------------------------------------------------

--------------------------------------------------------------------------------
                      *SEE INSTRUCTION BEFORE FILLING OUT!






CUSIP No. 416906105                  13G                      Page 3  of 7 Pages
   -------------






--------------------------------------------------------------------------------
1        NAME OF REPORTING PERSON
         S.S. OR I.R.S. IDENTIFICATION NO OF ABOVE PERSON
                                Robert E Kern Jr.


--------------------------------------------------------------------------------

2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                      (c)  / /

                                                                      (d)  / /

--------------------------------------------------------------------------------
3              SEC USE ONLY


--------------------------------------------------------------------------------
4        CITIZENSHIP OR PLACE OF ORGANIZATION


                          U.S.A.
--------------------------------------------------------------------------------

                         5        SOLE VOTING POWER

 NUMBER OF                             -
 SHARES BENEFICIALLY     -------------------------------------------------------
 OWNED BY                6        SHARED VOTING POWER
 EACH           
 REPORTING                        2,380,500  - (See Schedule Item 4 
 PERSON WITH                                   incorporated by reference)
                         -------------------------------------------------------
                         7        SOLE DISPOSITIVE POWER

                                        -
                         -------------------------------------------------------
                         8        SHARED DISPOSITIVE POWER
                          
                                  2,380,500   - (See Schedule Item 4 
                                                incorporated by reference)

--------------------------------------------------------------------------------
9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                                  2,380,500  - (See Schedule Item 4 
                                               incorporated by reference)
--------------------------------------------------------------------------------
10       CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                        -
--------------------------------------------------------------------------------
11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                                      7.8%
--------------------------------------------------------------------------------
12       TYPE OF REPORTING PERSON*

                                       IN

--------------------------------------------------------------------------------
                      *SEE INSTRUCTION BEFORE FILLING OUT!






CUSIP No. 416906105                              13G          Page 4 of 7  Pages
         -------------






--------------------------------------------------------------------------------
1        NAME OF REPORTING PERSON
         S.S. OR I.R.S. IDENTIFICATION NO OF ABOVE PERSON
                                  David G. Kern


--------------------------------------------------------------------------------

2 CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                 (e)   / /

                                                                 (f)   / /

--------------------------------------------------------------------------------
3        SEC USE ONLY


--------------------------------------------------------------------------------
4        CITIZENSHIP OR PLACE OF ORGANIZATION


                          U.S.A.
--------------------------------------------------------------------------------

                         5        SOLE VOTING POWER

 NUMBER OF                            -
 SHARES BENEFICIALLY     -------------------------------------------------------
 OWNED BY                6        SHARED VOTING POWER
 EACH           
 REPORTING                        2,380,500  - (See Schedule Item 4 
 PERSON WITH                                    incorporated by reference)
                         -------------------------------------------------------
                         7        SOLE DISPOSITIVE POWER

                                        -
                         -------------------------------------------------------
                         8        SHARED DISPOSITIVE POWER
                          
                                  2,380,500   - (See Schedule Item 4 
                                                incorporated by reference)

--------------------------------------------------------------------------------
9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                                  2,380,500  - (See Schedule Item 4 
                                               incorporated by reference)
--------------------------------------------------------------------------------
10       CHECK IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                        -
--------------------------------------------------------------------------------
11       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                                     7.8%
--------------------------------------------------------------------------------
12       TYPE OF REPORTING PERSON*

                                      IN
--------------------------------------------------------------------------------

--------------------------------------------------------------------------------
                      *SEE INSTRUCTION BEFORE FILLING OUT!






CUSIP NO. 416906105                       SCHEDULE 13G       Page  5 of  7 Pages



ITEM  1 (a).   NAME OF ISSUER:
               Harvard BioScience Inc.

ITEM  1 (b).   ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:
               84 October Hill Rd
               Holliston, MA 01746

ITEM  2 (c).   NAME OF PERSON FILING:
               Kern Capital Management, LLC ("KCM"), Robert E. Kern Jr.(R. Kern)
               and David G. Kern (D. Kern). R. Kern, D. Kern are Principals 
               and controlling members of KCM.

ITEM  2 (b).   ADDRESS OR PRINCIPAL BUSINESS OFFICE OR, IF NONE, RESIDENCE:
               The address of the principal business office of each reporting 
               person is: 114 West 47th Street, Suite 1926, New York, NY 10036.


ITEM  2 (c).   CITIZENSHIP:
               Reference  is made to Item 4 of each of the cover page of this
               Schedule, which Items are incorporated by reference herein.

ITEM 2 (d).    TITLE OF CLASS OF SECURITIES:
               Common Stock

ITEM 2 (e).    CUSIP NUMBER:
               416906105

ITEM 3 (e)     THE PERSONS FILING THIS SCHEDULE, PURSUANT TO
               PARAGRAPH 240.13d-1(b)  ARE A:
               (X)  Investment  Advisor  registered  under section 203 of the
               Investment Advisors Act of 1940.

ITEM 4.        OWNERSHIP:
               Reference  is made to Items  5-9 and 11 of cover  pages  which
               Items are incorporated by reference herein.

               R.  Kern  and D.  Kern as  controlling  members  of KCM may be
               deemed the  beneficial  owner of the securities of the company
               owned by KCM as of  December 31, 2004 in that they  might be
               deemed to share the power to direct the voting or  disposition
               of the securities. Neither the filing of this Schedule nor any
               of its  contents  shall be deemed to  constitute  an admission
               that  either  R.  Kern or D.  Kern is,  for any  purpose,  the
               beneficial owner of any such securities to which this Schedule
               relates, and such beneficial ownership is expressly denied.







CUSIP NO. 416906105                    SCHEDULE 13G          Page  6 of  7 Pages




ITEM 5.        OWNERSHIP OF MORE THAN FIVE PERCENT OR LESS OF A CLASS:
               If this statement is being filed to report the fact that as of
               the date here of the  reporting  person  has  ceased to be the
               beneficial  owner of more  than five  percent  of the class of
               securities, check the following / /.

               Not applicable.

ITEM 6.        OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON:
               The shares reported are held in institutional accounts for the
               economic benefit of the beneficiaries of those accounts.

ITEM 7.        IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH 
               ACQUIRED THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING 
               COMPANY:

               Not applicable.

ITEM 8.        IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP:
               Not applicable.

ITEM 9.        NOTICE OF DISSOLUTION OF GROUP:
               Not applicable.

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
               SUCH THE  SECURITIES AND WERE NOT ACQUIRED AND ARE NOT HELD IN
               CONNECTION WITH OR AS A PARTICIPANT IN ANY TRANSACTION  HAVING
               SUCH PURPOSES 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.


February 14, 2005                         /s/ John J. Crimmins
---------------------------         By:   --------------------------------------
         DATED                            John J. Crimmins
                                          Senior Vice President
                                          Chief Financial & Operations Officer
                                          Kern Capital Management LLC

                                          /s/ Robert E. Kern Jr.
                                    By:   --------------------------------------
                                          Robert E. Kern Jr.

                                          /s/ David G. Kern
                                    By:   --------------------------------------
                                          David G. Kern







CUSIP NO. 416906105            SCHEDULE 13G                Page  7  of  7  Pages





                                    EXHIBIT 1

                  AGREEMENT AS TO JOINT FILING OF SCHEDULE 13G



This  agreement is made pursuant to Rule  13d-1(f)(1)  under the  Securities and
Exchange Act of 1934,  as amended (the "Act"),  by and among the parties  listed
below,  each referred to herein as "Joint Filer".  The Joint Filers agree that a
statement of  beneficial  ownership as required by Section  13(d) of the Act and
the Rules  thereunder  may be filed on each of their  behalf on Schedule 13G and
that said joint filing may thereafter be amended by further joint  filings.  The
Joint Filers state that they each  satisfy the  requirements  for making a joint
filing under rule 13d-1.



February 14, 2005                   /s/ John J. Crimmins
-------------------         By:   ----------------------------------------------
    DATED                               John J. Crimmins
                                        Senior Vice President
                                        Chief Financial & Operations Officer
                                        Kern Capital Management LLC

                                    /s/ Robert E. Kern Jr.
                            By:   ----------------------------------------------
                                        Robert E. Kern Jr.

                                    /s/ David G. Kern
                            By:   ----------------------------------------------
                                        David G. Kern