<PAGE>   1
   As filed with the Securities and Exchange Commission on November 24, 1998

                                                     Registration No. 333-______


                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                          -----------------------------

                                    FORM S-8
                             REGISTRATION STATEMENT
                                      UNDER
                           THE SECURITIES ACT OF 1933
                          -----------------------------

                          SPEEDFAM INTERNATIONAL, INC.
               (Exact name of issuer as specified in its charter)

                Illinois                                          36-2421613
     (State or other jurisdiction of                           (I.R.S. Employer
     incorporation or organization)                          Identification No.)

          305 North 54th Street                                     85226
            Chandler, Arizona                                     (Zip Code)
(Address of principal executive offices)

                        1995 EMPLOYEE STOCK PURCHASE PLAN
                         OF SPEEDFAM INTERNATIONAL, INC.
                            (Full title of the plan)

        Roger K. Marach                             Copies of Communications to:
Treasurer, Assistant Secretary                            Jonathan A. Koff
  and Chief Financial Officer                            Chapman and Cutler
     305 North 54th Street                             111 West Monroe Street
       Chandler, Arizona                               Chicago, Illinois 60603
        (602) 705-2100                                     (312) 845-3000
 (Name, address and telephone
 number of agent for service)
                          -----------------------------
                         CALCULATION OF REGISTRATION FEE

<TABLE>
<CAPTION>
----------------------------------------------------------------------------------------------------------------------
              TITLE OF SECURITIES                    AMOUNT          PROPOSED          PROPOSED         AMOUNT OF
               TO BE REGISTERED                      TO BE            MAXIMUM          MAXIMUM        REGISTRATION
                                                 REGISTERED(1)       OFFERING         AGGREGATE            FEE
                                                                     PRICE PER         OFFERING
                                                                     SHARE(2)           PRICE
----------------------------------------------------------------------------------------------------------------------
<S>                                              <C>                  <C>             <C>                <C>   
Common Stock without par value..............     500,000 Shares       $14.72          $7,360,000         $2,047
======================================================================================================================
</TABLE>

(1)  Pursuant to Rule 416, this Registration Statement also covers an
     indeterminate number of shares as may be issued as a result of the
     anti-dilution provisions of the Plan.

(2)  Pursuant to Rule 457(c) and (h), the proposed maximum offering price per
     share and maximum aggregate offering price and amount of registration fee
     are calculated based upon a price per share of $14.72, the average of the
     high and low price for the shares of SpeedFam International, Inc. Common
     Stock as reported by the Nasdaq Stock Market National Market System on
     November 19, 1998, a date within five business days prior to the date of
     filing the Registration Statement.




<PAGE>   2
                                EXPLANATORY NOTE

         This Registration Statement is being filed by SpeedFam International,
Inc. (the "Company"), pursuant to General Instruction E to Form S-8, with
respect to the registration of additional securities of the same class as other
securities for which the Company's Registration Statement on Form S-8
(Registration No. 33-98026) relating to the 1995 Employee Stock Purchase Plan of
SpeedFam International, Inc. (the "1995 Purchase Plan") was filed with the
Securities and Exchange Commission (the "Commission") on October 11, 1995, and
which is incorporated herein by reference. On October 8, 1998, the shareholders
of the Company approved an increase in the maximum number of shares of the
Company's Common Stock which shall be available for sale under the 1995 Purchase
Plan from 500,000 shares to 1,000,000 shares. The additional 500,000 shares are
being registered under this Registration Statement.

         In accordance with the Note to Part I of Form S-8, the information
specified by Part I of Form S-8 has been omitted from this Registration
Statement.

PART II -- INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

Item 3.  Incorporation of Certain Documents by Reference

         The following documents which have been filed with the Securities and
Exchange Commission by the Company pursuant to the Securities Exchange Act of
1934 ("1934 Act") are incorporated herein by reference:

                  (a) The Company's Registration Statement on Form S-8
         (Registration No. 33-98026).

                  (b) The Company's Annual Report on Form 10-K for the fiscal
         year ended May 31, 1998 (1934 Act File No. 0-26784).

                  (c) The Company's Quarterly Report on Form 10-Q filed October
         15, 1998 (1934 Act File No. 0-26784).

                  (d) The description of the Company's Common Stock which is
         contained in the Company's Form 8-A (File No. 0-26784) filed with the
         Commission on September 18, 1995.

         All documents subsequently filed by the Company pursuant to Sections
13(a), 13(c), 14 and 15(d) of the 1934 Act, prior to the filing of a
post-effective amendment which indicates that all securities offered hereby have
been sold or which deregisters all such securities then remaining unsold, shall
be deemed to be incorporated by reference into this Registration Statement and
to be a part hereof from the date of filing such documents.

                                      II-1
<PAGE>   3
Item 5.  Interest of Named Experts and Counsel

         The validity of the shares of Common Stock offered hereby will be
passed upon for the Company by Chapman and Cutler, Chicago, Illinois. Mr.
Charles A. Kelly, a partner of Chapman and Cutler, serves as Secretary of the
Company and owns 60,000 shares of the Company's Common Stock. In addition, Mr.
Kelly has sole voting and dispositive power over 627,070 shares of Common Stock
held in the Nancy Jo Farley Trust, a revocable trust, of which he serves as
co-trustee. Mr. Kelly also shares voting and dispositive power over 691,380
shares of Common Stock held in the Makoto Kouzuma Trust, a revocable trust, of
which he serves as co-trustee and over 168,380 shares of Common Stock held in
the SpeedFam Employees Profit Sharing Trust, of which he serves as co-trustee.

Item 6.  Indemnification of Directors and Officers

         Section 8.75 of the Illinois Business Corporation Act of 1983, as
amended, sets forth the conditions and limitations governing the indemnification
of officers, directors, and other persons. The Company's bylaws provide for
indemnification by the Company of directors, officers, employees or agents of
the Company to the full extent permitted by the above-mentioned section of the
Act.

         In addition, the Company maintains a directors' and officers' liability
insurance policy to insure its liability under the above-described provision of
its bylaws and to insure its individual directors and officers against certain
obligations not covered by such provisions.

Item 8.  Exhibits

         The following exhibits are submitted herewith or incorporated by
reference herein.

      EXHIBIT                     DESCRIPTION
      NUMBER

         4.1      First Amendment to the 1995 Employee Stock Purchase Plan of
                  SpeedFam International, Inc.
        
         4.2      1995 Employee Stock Purchase Plan of SpeedFam International,
                  Inc.

         4.3      Specimen Certificate

         5.1      Opinion of Chapman and Cutler

         24.1     Consent of Chapman and Cutler

         24.2     Consent of KPMG Peat Marwick LLP

         25.1     Power of Attorney




                                      II-2
<PAGE>   4
Item 9.  Undertakings

         (a)    The undersigned registrant hereby undertakes:

                   (1) To file, during any period in which offers or sales are
         being made, a post-effective amendment to this Registration Statement:

                           (i) To include any prospectus required by Section
                  10(a)(3) of the Securities Act of 1933;

                           (ii) To reflect in the prospectus any facts or events
                  arising after the effective date of the Registration Statement
                  (or the most recent post-effective amendment thereof) which,
                  individually or in the aggregate, represent a fundamental
                  change in the information set forth in the Registration
                  Statement; and

                          (iii) To include any material information with respect
                  to the plan of distribution not previously disclosed in the
                  Registration Statement or any material change to such
                  information in the Registration Statement.

                   (2) That, for the purpose of determining any liability under
         the Securities Act of 1933, each such post-effective amendment 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) To remove from registration by means of a post-effective
         amendment any of the securities being registered which remain unsold at
         the termination of the offering.

         (b) The undersigned registrant hereby undertakes that, for the purpose
of determining any liability under the Securities Act of 1933, each filing of
the registrant's annual report pursuant to Section 13(a) or Section 15(d) of the
Securities Exchange Act of 1934 (and, where applicable, each filing of an
employee benefit plan's annual report pursuant to Section 15(d) of the
Securities Exchange Act of 1934) that is incorporated by reference in the
Registration Statement 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.

         (c) Insofar as indemnification for liabilities arising under the
Securities Act of 1933 may be permitted to directors, officers and controlling
persons of the registrant pursuant to the foregoing provisions, 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 of 1933 and is, therefore, unenforceable. In the event
that a claim for indemnification against such liabilities (other than the
payment by 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 by it is against public policy as expressed in the
Securities Act of 1933 and will be governed by the final adjudication of such
issue.



                                      II-3
<PAGE>   5
                                   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-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the Town of Chandler, State of Arizona, on November 24, 1998.

                   SPEEDFAM INTERNATIONAL, INC.



                   By                 /s/ Roger K. Marach
                          -----------------------------------------------------
                                         Roger K. Marach,
                                  Treasurer, Assistant Secretary
                                   and Chief Financial Officer
                           (Principal financial and accounting officer)


                                POWER OF ATTORNEY

         Each person whose signature appears below hereby constitutes and
appoints Roger K. Marach and Richard J. Faubert, and each of them, his true and
lawful attorneys-in-fact and agents, with full power and substitution and
resubstitution for him or her in his or her name, place and stead, in any and
all capacities to sign any and all pre-effective and/or post-effective
amendments to this Registration Statement and to file the same, with all
exhibits thereto, and other documents in connection therewith with the
Securities and Exchange Commission under the Securities Act of 1933.

         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 November 24, 1998.

      SIGNATURE                                   TITLE


 /s/ James N. Farley
   James N. Farley                        Chairman and Director


/s/ Richard J. Faubert
  Richard J. Faubert                President, Chief Executive Officer
                                               and Director
                                      (principal executive officer)


 /s/ Makoto Kouzuma
    Makoto Kouzuma                      Vice Chairman and Director


                                      II-4
<PAGE>   6

 /s/ Roger K. Marach
   Roger K. Marach                  Treasurer, Assistant Secretary and
                                         Chief Financial Officer
                                      (principal financial officer)


  /s/ Neil R. Bonke
    Neil R. Bonke                                Director

   Stuart L. Meyer                               Director


 /s/ Robert M. Miller
   Robert M. Miller                              Director

   Richard S. Hill                               Director




                                      II-5
<PAGE>   7
                                 Exhibit Index

     EXHIBIT                                 DESCRIPTION                     
     NUMBER                                                                  
                                                                             

       4.1          First Amendment of the 1995 Employee Stock Purchase Plan of
                    SpeedFam International, Inc.................................

       4.2          1995 Employee Stock Purchase Plan of SpeedFam
                    International, Inc. (filed as Exhibit 10.11 to the
                    Company's Registration Statement on Form S-1 (Registration
                    No. 33-95628), and incorporated herein by reference)........

       4.3          Specimen Certificate (filed as an exhibit to the Company's
                    Form 8-A (File No. 0-26784) filed with the Commission on
                    September 18, 1995, and incorporated herein by reference)...

       5.1          Opinion of Chapman and Cutler...............................

      24.1          Consent of Chapman and Cutler (included in Exhibit 5.1).....

      24.2          Consent of KPMG Peat Marwick LLP............................

      25.1          Power of Attorney (set forth on page II-4 of this
                    Registration Statement).....................................