<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 STOCK PLAN FOR EMPLOYEES AND DIRECTORS
                         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....    800,000 Shares    $14.72       $11,766,000     $3,271
================================================================================================
</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.
33-98568) relating to the 1995 Stock Plan for Employees and Directors of
SpeedFam International, Inc. (the "1995 Stock Plan") was filed with the
Securities and Exchange Commission (the "Commission") on October 25, 1995, and
which is incorporated herein by reference. On October 8, 1998, the shareholders
of the Company approved an increase in the maximum aggregate number of shares of
the Company's Common Stock as to which awards of options, restricted shares,
units or rights may be made from time to time under the 1995 Stock Plan from
1,000,000 shares to 1,800,000 shares. The additional 800,000 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.
     33-98568).

          (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 Stock Plan for Employees and
              Directors of SpeedFam International, Inc.

     4.2      1995 Stock Plan for Employees and Directors 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;

             (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                    DESCRIPTION                     PAGE NUMBER IN
   NUMBER                                                      SEQUENTIAL
                                                            NUMBERING SYSTEM

     4.1      First Amendment to the 1995 Stock Plan
              for Employees and Directors of SpeedFam
              International, Inc.......................

     4.2      1995 Stock Plan for Employees and
              Directors of SpeedFam International,
              Inc. as amended as of May 22, 1997
              (filed as Exhibit 10.11 to the Company's
              Form 10-K for fiscal year 1997 (File No.
              0-26784), 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).....