<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT

                       PURSUANT TO SECTION 13 OR 15(d) OF
                       THE SECURITIES EXCHANGE ACT OF 1934

       DATE OF REPORT (DATE OF EARLIEST EVENT REPORTED): NOVEMBER 19, 1998


                       INTEGRATED PROCESS EQUIPMENT CORP.
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

<TABLE>
<S>                               <C>                        <C>       
           DELAWARE                       0-20470                        77-0296222
(STATE OR OTHER JURISDICTION OF   (COMMISSION FILE NUMBER)   (I.R.S. EMPLOYER IDENTIFICATION NO.)
 INCORPORATION OR ORGANIZATION)
</TABLE>

                                 911 BERN COURT
                               SAN JOSE, CA 95112
          (ADDRESS, INCLUDING ZIP CODE, OF PRINCIPAL EXECUTIVE OFFICES)

       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (408) 436-2170

                                 NOT APPLICABLE
          (FORMER NAME OR FORMER ADDRESS, IF CHANGED SINCE LAST REPORT)
<PAGE>   2
Item 5. Other Events

      On November 19, 1998, the Company and SpeedFam International, Inc.
("SpeedFam") entered into an Agreement and Plan of Merger among IPEC, SpeedFam
and SpeedFam, Inc. ("Merger Sub"), a wholly-owned subsidiary of SpeedFam,
providing for the merger of the Company with Merger Sub (the "Merger"). Upon
consummation of the Merger, the surviving corporation of the Merger will be a
wholly-owned subsidiary of SpeedFam.


Item 7.   Financial Statements, Pro Forma Financial Information and Exhibits

     2.1  Agreement and Plan of Merger, dated November 19, 1998, by and among
          the Company, SpeedFam International, Inc. ("SpeedFam") and SpeedFam,
          Inc., a wholly-owned subsidiary of SpeedFam.

     2.2  Stock Option Agreement, dated November 19, 1998, between the Company
          and SpeedFam.

     2.3  Stock Option Agreement, dated November 19, 1998, between SpeedFam and
          the Company.

     99.1 Press Release, dated November 19, 1998. 

                                      -2-
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      Pursuant to the requirements of the Securities Exchange Act of 1934,
Integrated Process Equipment Corp. has duly caused this report to be signed on
its behalf by the undersigned hereunto duly authorized.

                                  Integrated Process Equipment Corp.


                                  By: /s/ John S. Hodgson
                                      ------------------------------------------
                                      John S. Hodgson
                                      Vice President and Chief Financial Officer



Date: November 23, 1998
<PAGE>   4
                                 EXHIBIT INDEX

Exhibit
  No.                               Description
-------                             ----------- 
  2.1    Agreement and Plan of Merger, dated November 19, 1998, by and among the
         Company, SpeedFam International, Inc. ("SpeedFam") and SpeedFam, Inc.,
         a wholly-owned subsidiary of SpeedFam.

  2.2    Stock Option Agreement, dated November 19, 1998, between the Company
         and SpeedFam.

  2.3    Stock Option Agreement, dated November 19, 1998, between SpeedFam and
         the Company.

 99.1    Press Release, dated November 19, 1998.