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<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):    SEPTEMBER 26, 2001


                               CISCO SYSTEMS, INC.
               (Exact Name of Registrant as Specified in Charter)




<TABLE>
<CAPTION>
         CALIFORNIA                                0-18225                             77-0059951
<S>                                              <C>                              <C>
(State or Other Jurisdiction                     (Commission                         (IRS Employer
      of Incorporation)                           File Number)                     Identification No.)


170 WEST TASMAN DRIVE, SAN JOSE, CALIFORNIA                                            95134-1706
(Address of Principal Executive Offices)                                               (Zip Code)
</TABLE>




Registrant's telephone number, including area code:  (408) 526-4000

<PAGE>   2


ITEM 5. OTHER EVENTS.

     On September 26, 2001, Cisco Systems, Inc. (the "Registrant") announced
that it completed the acquisition of Allegro Systems, Inc., a Delaware
corporation. A copy of the press release issued by the Registrant on September
26, 2001 concerning the foregoing transaction is filed herewith as Exhibit 99.1
and is incorporated herein by reference.

ITEM 7. FINANCIAL STATEMENTS, PRO FORMA FINANCIAL INFORMATION AND EXHIBITS.

     (c)  Exhibits.

          99.1  Press Release of Registrant, dated September 26,
                2001, announcing Registrant's completion of the
                acquisition of Allegro Systems, Inc.

<PAGE>   3

                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.

                                        CISCO SYSTEMS, INC.

Dated:  September 27, 2001              By: /s/ Daniel Scheinman
                                        ----------------------------------------
                                        Daniel Scheinman
                                        Senior Vice President, Corporate Affairs
<PAGE>   4

                                  EXHIBIT INDEX
<TABLE>
<CAPTION>
Exhibit
Number                       Description of Document
-------                      -----------------------
<S>           <C>
99.1          Press Release of Registrant, dated September 26, 2001, announcing
              Registrant's completion of the acquisition of Allegro Systems, Inc.
</TABLE>

</TEXT>
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<DOCUMENT>
<TYPE>EX-99.1
<SEQUENCE>3
<FILENAME>f76031ex99-1.txt
<DESCRIPTION>EXHIBIT 99.1
<TEXT>
<PAGE>   1
                                                                    EXHIBIT 99.1
                                                                   PRESS RELEASE

PRESS CONTACT:                                INVESTOR RELATIONS CONTACT:
Robyn Jenkins                                 Roberta DeTata
Cisco Systems, Inc.                           Cisco Systems, Inc.
(408) 853-9848                                (408) 527-6388
rojenkin@cisco.com                            rdetata@cisco.com

INDUSTRY ANALYST CONTACT:
Leslie Fletcher
Cisco Systems, Inc.
(408) 853-6289
fletcher@cisco.com

             CISCO SYSTEMS COMPLETES ACQUISITION OF ALLEGRO SYSTEMS

     SAN JOSE, Calif., Sept. 26, 2001 - Cisco Systems, Inc., today announced it
has completed the acquisition of privately held Allegro Systems, Inc.

     On July 27, 2001, Cisco announced a definitive agreement to acquire
Allegro Systems, a developer of Virtual Private Network (VPN) acceleration
technologies designed to enhance the performance and functionality of secure
networking technologies. The acquisition strengthens Cisco's existing VPN and
security solutions with added performance capabilities to meet the growing
requirements of organizations connecting remote offices, employees and customers
to corporate networks and the Internet. The acquisition of Allegro Systems is
being accounted for as a purchase.

ABOUT CISCO SYSTEMS

     Cisco Systems (NASDAQ: CSCO) is the worldwide leader in networking for the
Internet. Cisco news and information are available at http://www.cisco.com.


                                      # # #

Cisco, Cisco Systems, PIX, IOS and the Cisco Systems logo are registered
trademarks of Cisco Systems, Inc. or its affiliates in the U.S. and certain
other countries. All other trademarks mentioned in this document are the
property of their respective owners. The use of the word partner does not imply
a partnership relationship between Cisco and any other company. (0005R)

</TEXT>
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