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                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                            ________________________





                                    FORM 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER
                    PURSUANT TO RULE 13a-16 OR 15d-16 OF THE
                        SECURITIES EXCHANGE ACT OF 1934


                      For the month of October 31, 1997



                            ________________________





                                   OLICOM A/S
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)


                                  NYBROVEJ 114
                                 DK-2800 LYNGBY
                                    DENMARK
                    (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)



                       __________________________________


          [Indicate by check mark whether the registrant files or will
           file annual reports under cover of Form 20-F or Form 40-F.

                          Form 20-F   X      Form 40-F

  [Indicate by check mark whether the registrant by finishing the information
    contained in this Form is also thereby furnishing the information to the
  Commission pursuant to Rule 13g3-2(b) under the Securities Exchange Act of
                                     1934.

                               Yes         No   X

 [If "Yes" is marked, indicate below the file number assigned to the registrant
 in connection with Rule 13g3-2(b):  Not Applicable


      This Form 6-K shall be incorporated by reference to the registrant's
      registration statement on Form F-4 under the Securities Act of 1933,
                    as amended, registration no. 333-24655.
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                    INFORMATION TO BE INCLUDED IN THE REPORT


Item 1.  Intention to List on the Copenhagen Stock Exchange.

         Olicom A/S ("Olicom") has announced that, subject to market and other
conditions, it intends to have its shares listed on the Copenhagen Stock
Exchange in November 1997. In connection with the listing, approximately 1.8
million shares are expected to be offered for sale only to European investors.
The offering will be managed by an international consortium of underwriters.

         Most of the shares will be made available by existing shareholders
including Nilex Systems ApS ("Nilex"), an affiliate of Olicom's founder,
president and chief executive officer Lars Stig Nielsen. Nilex currently
anticipates selling up to 700,000 shares. Approximately 50,000 of the shares
will be Olicom treasury shares. The offering will also include an option for
the underwriters to purchase an additional 270,000 Olicom treasury shares to
cover over-allotments, if any.

         The shares to be offered will not be registered under the Securities
Act of 1933, as amended, or applicable state securities laws, and may not be
offered or sold absent registration under the Securities Act and applicable
state securities laws or available exemptions from registration requirements.
The shares will be offered and sold only outside the United States to persons
who are not U.S. persons, and the prospectus will not be distributed anywhere
in the U.S. nor to any U.S. person.

         A copy of the press release announcing the foregoing is attached as
Exhibit 99.1 and is incorporated herein by reference.


Item 2.  Exhibits.

Exhibit No.           Description

  99.1                Press Release dated October 3, 1997, announcing the
                      intention of Olicom to have its shares listed on the
                      Copenhagen Stock Exchange.





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                                   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, thereunto duly authorized.


                                             OLICOM A/S



Date: October 15, 1997                       By:   /s/ Boje Rinhart
                                                --------------------------------
                                                Boje Rinhart,
                                                Chief Financial Officer






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                                 EXHIBIT INDEX


Exhibit No.            Description
- -----------            -----------      
   99.1                Press Release dated October 3, 1997, announcing the
                       intention of Olicom to have its shares listed on the
                       Copenhagen Stock Exchange.





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