<PAGE>   1
 
   
    AS SUBMITTED TO THE SECURITIES AND EXCHANGE COMMISSION ON MARCH 4, 1997
    
 
                                                      REGISTRATION NO. 333-18121
================================================================================
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington D.C. 20549
                      ------------------------------------
 
   
                               AMENDMENT NO. 5 to
    
                                    FORM S-1
                          Registration Statement Under
                           The Securities Act of 1933
                      ------------------------------------
                             EURONET SERVICES INC.
             (Exact Name of Registrant as Specified in its Charter)
 

<TABLE>
<S>                                 <C>                                 <C>
            DELAWARE                              6099                             74-2806888
(State or Other Jurisdiction of       (Primary Standard Industrial              (I.R.S. Employer
 Incorporation or Organization)       Classification Code Number)             Identification No.)
</TABLE>

 
                                ZSIGMOND TER 10
                                H-1023 Budapest
                                    Hungary
                                011-361-335-1224
   (Address and telephone number of Registrant's principal executive offices)
 
                             CT CORPORATION SYSTEM
                                 1633 Broadway
                            New York, New York 10019
                                 (212) 664-7666
           (Name, address and telephone number of agent for service)
                      ------------------------------------
                                   COPIES TO:
 

<TABLE>
<S>                                                <C>
               JAMES M. BARTOS, ESQ.                               CARTER STRONG, ESQ.
                Shearman & Sterling                         Arent Fox Kintner Plotkin & Kahn
                  199 Bishopsgate                             1050 Connecticut Avenue, N.W.
              London EC2M 3TY England                            Washington, D.C. 20036
</TABLE>

 
                      ------------------------------------
 
     Approximate date of commencement of proposed sale to the public: As soon as
practicable after the effective date of this Registration Statement.
                      ------------------------------------
 
     If any of the securities being registered on this form are to be offered on
a delayed or continuous basis pursuant to Rule 415 under the Securities Act of
1933, please check the following box.  [ ]
 
     If this Form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, please check the following box
and list the Securities Act registration statement number of the earlier
effective registration statement for the same offering.  [ ]
 
     If this Form is a post-effective amendment filed pursuant to Rule 462(c)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the same offering.  [ ]
 
     If delivery of the prospectus is expected to be made pursuant to Rule 434,
please check the following box.  [ ]
                      ------------------------------------
 
     THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(A) OF
THE SECURITIES ACT OF 1933 OR UNTIL THE REGISTRATION STATEMENT SHALL BECOME
EFFECTIVE ON SUCH DATE AS THE COMMISSION, ACTING PURSUANT TO SAID SECTION 8(A),
MAY DETERMINE.
================================================================================

<PAGE>   2
 
   
                                EXPLANATORY NOTE
    
 
   
     The sole purpose of this Amendment No. 5 is to file an exhibit previously
omitted from the Registration Statement. Accordingly, this Amendment No. 5
consists only of the facing page, this note and Part II of the Registration
Statement. The Prospectus is unchanged and has been omitted.
    

<PAGE>   3
 

                                    PART II
 
                     INFORMATION NOT REQUIRED IN PROSPECTUS
 

ITEM 13.  OTHER EXPENSES OF ISSUANCE AND DISTRIBUTION.
 
     The following table sets forth the Registrant's estimated expenses in
connection with the issuance and distribution of the securities being
registered, other than underwriting discounts and commissions.
 

<TABLE>
    <S>                                                                        <C>
    Securities and Exchange Commission registration fee.....................   $  25,858
    Nasdaq National Market quotation fee....................................      30,750
    National Association of Securities Dealers, Inc. filing fee.............       9,000
    Reimbursement of Underwriters' Expenses.................................   1,000,000
    Legal fees and expenses.................................................      80,000
    Accounting fees and expenses............................................      90,000
    Blue sky qualification fees and expenses................................      15,000
    Transfer agent fees and expenses........................................       5,000
                                                                               ----------
         Total..............................................................   $1,255,608
                                                                               ==========
</TABLE>

 

ITEM 14.  INDEMNIFICATION OF DIRECTORS AND OFFICERS.
 
     Articles Eighth and Ninth of the Company's Certificate of Incorporation
provide as follows:
 
"EIGHTH:  The Corporation shall indemnify each of the individuals who may be
          indemnified to the fullest extent permitted by Section 145 of the
          General Corporation Law of the State of Delaware, as it may be amended
          from time to time ("Section 145"), (i) in each and every situation
          where the Corporation is obligated to make such indemnification
          pursuant to Section 145, and (ii) in each and every situation where,
          under Section 145, the Corporation is not obligated, but is permitted
          or empowered, to make such indemnification. The Corporation shall
          promptly make or cause to be made any determination which Section 145
          requires.
 
NINTH:     A director of the Corporation shall not be personally liable to the
          Corporation or its stockholders for monetary damages for breach of
          fiduciary duty as a director. This provision shall not eliminate or
          limit the liability of a director (i) for any breach of the director's
          duty of loyalty to the Corporation or its stockholders, (ii) for acts
          or omissions not in good faith or which involve intentional misconduct
          or a knowing violation of law, (iii) under Section 174 of the General
          Corporation Law of the State of Delaware, or (iv) for any transaction
          from which the director derived any improper personal benefit. If the
          General Corporation Law of the State of Delaware is subsequently
          amended to further eliminate or limit the liability of the director,
          then a director of the Corporation, in addition to the circumstances
          in which a director is not personally liable as set forth in the
          preceding sentence, shall not be liable to the fullest extent
          permitted by the amended General Corporation Law of the State of
          Delaware."
 
     Article VII of the Company's By-laws provides as follows:
 
     "Section 1  INDEMNIFICATION AND EXCULPATION.  Reference is hereby made to
                 Section 145 of the General Corporation Law of the State of
                 Delaware (or any successor provision thereto). The Corporation
                 shall indemnify each person who may be indemnified (the
                 "Indemnitees") pursuant to such section to the full extent
                 permitted thereby. In each and every situation where the
                 Corporation may do so under such section, the Corporation
                 hereby obligates itself to so indemnify the Indemnitees, and in
                 each case, if any, where the Corporation must make certain
                 investigations on a case-by-case basis prior to
                 indemnification, the Corporation hereby obligates itself to
                 pursue such investigation diligently, it being the specific
                 intention of these Bylaws to obligate the Corporation to
                 indemnify each person whom it may indemnify to the fullest
                 extent permitted by law at any time and from time to time. To
                 the extent not prohibited by Section 145 of the General
                 Corporation Law of the State of Delaware (or any other
 
                                      II-1

<PAGE>   4
 
provision of the General Corporation Law of the State of Delaware), the
Indemnitees shall not be liable to the Corporation except for their own
individual willful misconduct or actions taken in bad faith. Expenses incurred
              by an officer or director in defending any action, suit or
              proceeding shall be paid by the Corporation in advance of the
              final disposition of such action, suit or proceeding to the
              fullest extent permitted by subsection (e) of Section 145."
 
     Reference is also made to Section 5 of the Underwriting Agreement filed as
Exhibit 1.1 hereto.
 

ITEM 15.  RECENT SALES OF UNREGISTERED SECURITIES.
 
     On December 17, 1996, the Company and the shareholders and optionholders of
Euronet Holding N.V. entered into an Exchange Agreement pursuant to which (i)
9,585,569 shares of Common Stock of the Company will be issued to the
Shareholders of Euronet Holding N.V. in exchange for all of Common Shares of
Euronet Holding N.V. (ii) options to acquire 3,113,355 shares of Common Stock
will be granted to the holders of options to acquire 3,113,355 Common Shares of
Euronet Holding N.V. in exchange for all of such options and (iii) awards with
respect to 800,520 shares of Common Stock will be issued to the holders of
awards with respect to 800,520 preferred shares of Euronet Holding N.V. in
exchange for all such awards. Euronet Holding N.V. will be dissolved following
the consummation of the Offering. Such exchange is subject to and will be
effective upon the execution of the underwriting agreement to be executed in
connection with the Offering.
 

ITEM 16.  EXHIBITS AND FINANCIAL STATEMENT SCHEDULES.
 
     The following exhibits are filed as part of this Registration Statement:
 
   

<TABLE>
<CAPTION>
EXHIBIT
NUMBER                                   DESCRIPTION
- ------   ---------------------------------------------------------------------------
<C>      <S>
 +1.1    Form of Underwriting Agreement.
 +3.1    Certificate of Incorporation.
 +3.2    By-Laws of the Company.
 +4.1    Specimen of certificate for Shares, par value $0.02, of the Company.
 +5.1    Opinion of Arent Fox Kintner Plotkin & Kahn as to legality of the Shares.
+10.1    Amended Agreement for Solution Delivery dated April 17, 1996 between Bank
         Access 24 Rt. and IBM World Trade Corporation.
+10.2    Frame Contract dated February 20, 1996 between Bankomat 24 Sp. z o.o. and
         AT&T Global Information Solutions Polska, Sp. z o.o.
+10.3    Exchange Agreement dated as of December 17, 1996 among the Company and the
         stockholders and optionholders of Euronet Holding N.V.
+10.4    The Euronet Long-Term Incentive Plan.
+10.5    Employment Agreement of Mr. Brown.
+10.6    Form of Employment Agreement for Executive Officers.
+10.7    Subscription Agreement dated February 3, 1997 between Euronet Holding N.V.
         and General Electric Capital Corporation.
+21.1    List of Subsidiaries of Registrant.
 23.1    Consent of KPMG Polska Sp. z o.o.
+23.2    Consent of Arent Fox Kintner Plotkin & Kahn (included in Exhibit 5.1).
+24.1    Power of Attorney (included in signatures).
</TABLE>

    
 
- ---------------
 
+Previously filed.
 
                                      II-2

<PAGE>   5
 

ITEM 17.  UNDERTAKINGS.
 
     Insofar as indemnification for liabilities arising under the Securities Act
may be permitted to directors, officers and controlling persons of the
Registrant pursuant to the provisions described under "Item 14, Indemnification
of Directors and Officers" above, or otherwise, the Registrant has been advised
that in the opinion of the Securities and Exchange Commission such
indemnification is against public policy as expressed in the Securities Act and
is, therefore, unenforceable. In the event that a claim for indemnification
against such liabilities (other than the payment to the Registrant of expenses
incurred or paid by a director, officer or controlling person of the Registrant
in the successful defense of any action, suit or proceeding) is asserted by such
director, officer or controlling person in connection with the securities being
registered, the Registrant will, unless in the opinion of its counsel the matter
has been settled by controlling precedent, submit to a court of appropriate
jurisdiction the question whether such indemnification is against public policy
as expressed in the Securities Act and will be governed by the final
adjudication of such issue.
 
     The undersigned Registrant hereby undertakes that:
 
          (1) For purposes of determining any liability under the Securities
     Act, the information omitted from the form of prospectus filed as part of
     this registration statement in reliance upon Rule 430A and contained in a
     form of prospectus filed by the Registrant pursuant to Rule 424(b)(1) or
     (4) or 497(h) under the Securities Act shall be deemed to be part of this
     registration statement as of the time it was declared effective.
 
          (2) For the purpose of determining any liability under the Securities
     Act, each post-effective amendment that contains a form of prospectus shall
     be deemed to be a new registration statement relating to the securities
     offered therein, and the offering of such securities at that time shall be
     deemed to be the initial bona fide offering thereof.
 
          (3) It will provide to the U.S. Underwriters at the closing specified
     in the Underwriting Agreement, certificates in such denominations and
     registered in such names as required by the U.S. Underwriters to permit
     prompt delivery to each purchaser.
 
                                      II-3

<PAGE>   6
 

                                   SIGNATURES
 
   
     Pursuant to the requirements of the Securities Act of 1933, the Registrant
certifies that it has reasonable grounds to believe that it meets all of the
requirements for filing on Form S-1 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in Budapest on the 4th day of March, 1997
    
 
                                          EURONET SERVICES INC.
 
                                          By:  /s/  DANIEL R. HENRY
                                             --------------------------
                                                Daniel R. Henry
 
   
     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons in the
capacities indicated on March 4, 1997 and such signatures may be in
counterparts:
    
 

<TABLE>
<CAPTION>
                    SIGNATURE                                        TITLE
- -------------------------------------------------  ------------------------------------------
<C>                                                <S>
                        *                          Chairman of the Board of Directors, Chief
- -------------------------------------------------  Executive Officer and President (principal
                Michael J. Brown                   executive officer)
 
              /s/  DANIEL R. HENRY                 Director and Chief Operating Officer
- -------------------------------------------------
                 Daniel R. Henry
                        *                          Director
- -------------------------------------------------
                Steven J. Buckley
 
                        *                          Director
- -------------------------------------------------
              Eriberto R. Scocimara
 
                        *                          Director
- -------------------------------------------------
               Andrzej Olechowski
 
                        *                          Director
- -------------------------------------------------
               Thomas A. McDonnell
 
                              *                    Director
- -------------------------------------------------
              Nicholas B. Callinan
 
                              *                    Chief Financial Officer and Chief
- -------------------------------------------------  Accounting Officer (principal financial
                  Bruce Colwill                    officer and principal accounting officer)
 
          *By:  /s/  DANIEL R. HENRY
              --------------------------
                 Daniel R. Henry
                Attorney-in-Fact
</TABLE>

 
                                      II-4

<PAGE>   7
 
                           (LOGO) Printed in London

<PAGE>   8
 

                                 EXHIBIT INDEX
 
   

<TABLE>
<CAPTION>
    EXHIBIT NUMBER                                  DESCRIPTION                                PAGE
    --------------      -------------------------------------------------------------------    ----
    <C>            <C>  <S>                                                                    <C>
              23.1  --  Consent of KPMG Polska Sp. z o.o. .................................
</TABLE>

    





<PAGE>   1
 
                                                                    EXHIBIT 23.1
 
The Board of Directors
Euronet Services Inc.:
 
     We consent to the use of our report included herein and to the reference to
our firm under the headings "Summary Consolidated Financial Data", "Selected
Consolidated Financial Statements" and "Experts" in the prospectus.
 
KPMG Polska Sp. z o.o.
 
Warsaw, Poland
   
March 4, 1997