SECURITIES AND EXCHANGE COMMISSION
                              Washington D.C. 20549




                                    FORM 6-K



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


                        For the month ended May 31, 2002


                          ----------------------------



                                   OLICOM A/S
                 (Translation of registrant's name into English)


                                  Nybrovej 110
                               DK-2800 Kgs. 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]



                                   OLICOM A/S
                                    FORM 6-K


ITEM 1   TENDER OFFER

         Olicom A/S (the "Company") has announced that it is offering to
acquire all common shares, nominal value DKK 0.25 ("Common Shares"), held by
holders of 1,000 or fewer Common Shares for US$1.10 per share in cash (the
"Offer"). The Offer is to purchase all, but not less than all, Common Shares
held by such shareholders. The Offer is directed to shareholders resident in the
United States, and is not being made to shareholders of the Company who hold
their Common Shares through the Danish Securities Centre or whose Common Shares
are deposited outside of the United States. The Company anticipates that its
purchase of Common Shares pursuant to the Offer should not exceed 425,000 Common
Shares.

         The Company reserves the right to extend or amend the Offer at any
time and from time to time, and to terminate the Offer at any time. The Offer is
not subject to any financing condition, and the Offer is scheduled to expire at
5:00 p.m., New York City time, on Wednesday, June 19, 2002, unless the Offer is
extended. The complete terms and conditions of the Offer are contained in the
Offer to Purchase, a copy of which is filed herewith as Exhibit 99.1. The Offer
is made only pursuant to the Offer to Purchase.

         The purposes of the Offer are (i) to enable holders of 1,000 or fewer
Common Shares to dispose of such Common Shares without incurring brokerage
commissions and (ii) to reduce the number of shareholders of the Company
resident in the United States. At such time as the number of holders of Common
Shares resident in the United States decreases to less than 300, the Company
anticipates that it will terminate the registration of the Common Shares under
United States securities laws. See "Offer to Purchase -- Purposes of the
Offer."

         This Report on Form 6-K includes materials distributed to shareholders
of the Company in connection with the Offer.

         This Report contains statements that constitute "forward-looking
statements" within the meaning of Section 21E of the Securities Exchange Act of
1934, as amended. The Private Securities Litigation Reform Act of 1995 provides
a "safe harbor" for forward-looking information to encourage companies to
provide prospective information about themselves without fear of litigation so
long as the information is identified as forward looking and is accompanied by
meaningful cautionary statements identifying important factors that could cause
actual results to differ materially from those projected in the information. The
words "anticipate," "believe," "expect," "estimate," "intend," "plan," "should,"
"could," "may," "objective," "target," "goal" and "strategy" (or the negatives
of such terms) and other similar expressions are used in connection with
forward-looking statements. These forward-looking statements are based on
information currently available to the Company and are subject to a number of
risks, uncertainties and other factors that could cause the Company's actual
results, performance, prospects or opportunities to differ materially from those
expressed in, or implied by, these forward-looking statements. There can be no
assurance that forward-looking statements will approximate actual experience.

ITEM 2   EXHIBITS

        Exhibit 99.1      Offer to Purchase dated May 21, 2002.

        Exhibit 99.2      Letter of Transmittal.

        Exhibit 99.3      Notice of Guaranteed Delivery.

        Exhibit 99.4      Letter to Brokers, Dealers, Commercial Banks, Trust
                          Companies and Other Nominees.

        Exhibit 99.5      Letter to Clients for use by Brokers, Dealers,
                          Commercial Banks, Trust Companies and Other Nominees.

        Exhibit 99.6      Guidelines for Certification of Taxpayer
                          Identification Number on Substitute Form W-9.

        Exhibit 99.7      Letter to Shareholders from the President of the
                          Company.

        Exhibit 99.8      Press Release issued by the Company on May 22, 2002.




                                   SIGNATURES


The registrant certifies that it meets all of the requirements for filing and
has duly caused this form to be signed on its behalf by the undersigned,
thereunto duly authorized.



                                      Olicom A/S



Date:  May 22, 2002                   By: /s/  Boje Rinhart
                                          -------------------------------------
                                          Boje Rinhart
                                          President and Chief Executive Officer



                               INDEX TO EXHIBITS

<Table>
<Caption>
EXHIBIT
NUMBER                          DESCRIPTION
- ------                          -----------
               
Exhibit 99.1      Offer to Purchase dated May 21, 2002.

Exhibit 99.2      Letter of Transmittal.

Exhibit 99.3      Notice of Guaranteed Delivery.

Exhibit 99.4      Letter to Brokers, Dealers, Commercial Banks, Trust Companies
                  and Other Nominees.

Exhibit 99.5      Letter to Clients for use by Brokers, Dealers, Commercial
                  Banks, Trust Companies and Other Nominees.

Exhibit 99.6      Guidelines for Certification of Taxpayer Identification Number
                  on Substitute Form W-9.

Exhibit 99.7      Letter to Shareholders from the President of the Company.

Exhibit 99.8      Press Release issued by the Company on May 22, 2002.
</Table>