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

                                     SCHEDULE 13G

                       Under the Securities Exchange Act of 1934

                                  (Amendment No. )


                            MarketAxess Holdings Inc.
                               (Name of Issuer)
                                  Common Stock
                         (Title of Class of Securities)


                                   57060D108
                                 (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 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).




CUSIP No.     57060D108           13G                        Page 2 of 6  Pages


1.  NAME OF REPORTING PERSONS
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)
 
    The Bear Stearns Companies Inc.
        IRS# 13-3286161
________________________________________________________________________________
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

   SHARES                **
               _________________________________________________________________
BENEFICIALLY    6.   SHARED VOTING POWER

  OWNED BY            2,171,967*
               _________________________________________________________________
    EACH            7.   SOLE DISPOSITIVE POWER

  REPORTING            **
               _________________________________________________________________
   PERSON         8.   SHARED DISPOSITIVE POWER

    WITH                   2,171,967*
________________________________________________________________________________
9.    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                           2,171,967*
________________________________________________________________________________
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
                                                                          [_]
________________________________________________________________________________
11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                           9.84%
________________________________________________________________________________
12.  TYPE OF REPORTING PERSON*

                            HC,CO
________________________________________________________________________________


CUSIP No.    57060D108          13G                           Page 3 of 6 Pages


1.  NAME OF REPORTING PERSONS
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)
 
    Bear Market Access Corp.
        IRS# 13-4104634
________________________________________________________________________________
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

   SHARES               **
               _________________________________________________________________
BENEFICIALLY    6.   SHARED VOTING POWER

  OWNED BY            2,171,967*
               _________________________________________________________________
    EACH            7.   SOLE DISPOSITIVE POWER

  REPORTING           ** _______________________________________________________
   PERSON         8.   SHARED DISPOSITIVE POWER

    WITH                   2,171,967*
________________________________________________________________________________
9.    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                           2,171,967*
________________________________________________________________________________
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
                                                                          [_]
________________________________________________________________________________
11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                           9.84%
________________________________________________________________________________
12.  TYPE OF REPORTING PERSON*

                           CO
________________________________________________________________________________

* Consists of 1,599,999 shares of common stock and 571,968 shares of common 
stock issuable pursuant to warrants that are presently exercisable. The warrants
are issuable as common stock because the term of the warrants contains a 
limitation on acquiring shares of common stock if the conversion or exercise
would result in the holder beneficially owning more than 9.84% of issuer's 
outstanding shares of common stock.

CUSIP No.    57060D108       13G                              Page 4 of 6 Pages

Item 1(a).  Name of Issuer is       MarketAxess Holdings Inc. (the "Issuer").

Item 1(b).  The principal executive office of the Issuer is located at 140 
               Broadway 42 Floor, New York, NY 10005

Item 2(a).  The names of persons filing this statement are The Bear, Stearns 
               Companies Inc. and Bear Market Access Corp.

Item 2(b).  The principal business office of the Filer is located at 
                  383 Madison Avenue, New York, New York 10179.

Item 2(c).  The Filer is incorporated in Delaware.

Item 2(d).  This statement relates to shares of common stock of the Issuer.

Item 2(e).  The CUSIP number of the Securities is 57060D108.

Item 3.       If this statement is filed pursuant to 240.13d-1(b) or 
                  240.13d-2(b) or (c), check whether the person filing is a:

         (a)  [  ]  Broker or dealer registered under Section 15 of the Act 
                  (15 U.S.C.78o). (Bear Stearns & Co. Inc.)

                  (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)  [_]  An investment adviser in accordance with 
                            240.13d-1(b)(1)(ii)(E);

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

                  (g)  [X]  A parent holding company or control  person in 
                            accordance  with 240.13d-1(b)(1)(ii)(G) 
                            ( The Bear Stearns Companies Inc.);

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

         (i)   [_]   A 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 240.13d-1(b)(1)(ii)(J).

    If this statement is filed pursuant to 240.13d-1(c), check this box.   [_]


<PAGE>

CUSIP No.     57060D108             13G                      Page 5 of 6 Pages


Item 4.    Ownership As of January 31, 2004.

         (a)               2,171,967*
                  (b)               9.84%
                  (c)(i)   2,171,967*
                     (ii)  0
                     (iii) 2,171,967*
                     (iv)  0

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

               Not Applicable.

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.
           Bear Market Access Corp. is a wholly owned subsidiary of The Bear 
           Stearns Companies Inc.

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
              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 such purpose or effect.


















CUSIP No.     57060D108              13G                      Page 6 of 6 Pages


                                   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.

Date:   February 14, 2005


                          THE BEAR STEARNS COMPANIES INC.


 
                                            By:________________________________
                                                     Name:  Kenneth L. Edlow
                                                     Title:     Secretary



 

                              BEAR MARKET ACCESS CORP.


 
                                            By:________________________________
                                                     Name:  Ronald M. Hersch
                                                     Title:    President