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                                                                    Exhibit 4.13
 
THIS WARRANT AND THE SECURITIES RECEIVABLE UPON EXERCISE HEREOF HAVE NOT BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"),
OR ANY STATE SECURITIES LAW, AND MAY NOT BE SOLD, TRANSFERRED, PLEDGED,
HYPOTHECATED OR OTHERWISE DISPOSED OF OR EXERCISED UNLESS (i) A REGISTRATION
STATEMENT UNDER THE SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS SHALL
HAVE BECOME EFFECTIVE WITH REGARD THERETO, OR (ii) AN EXEMPTION FROM
REGISTRATION UNDER THE SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS IS
AVAILABLE IN CONNECTION WITH SUCH OFFER, SALE OR TRANSFER.

Warrant to Purchase
_______SHARES


                       WARRANT TO PURCHASE COMMON STOCK
                                      OF
                      ANCOR COMMUNICATIONS, INCORPORATED

     THIS CERTIFIES that ________________ or any subsequent ("Holder") hereof,
has the right to purchase from ANCOR COMMUNICATIONS, INCORPORATED, a Minnesota
corporation (the "Company"), up to ______ fully paid and nonassessable shares of
the Company's Common Stock, $.01 par value ("Common Stock"), subject to
adjustment as provided herein, at a price equal to the Exercise Price as defined
in Section 3 below, at any time beginning on the Date of Issuance and ending at
5:00 p.m., New York, New York time, on the date that is two (2) years following
the Date of Issuance (as defined below).

     The Holder of this Warrant agrees with the Company that this Warrant is
issued and all rights hereunder shall be held subject to all of the conditions,
limitations and provisions set forth herein.

     1.  Date of Issuance.
         -----------------

     This Warrant shall be deemed to be issued on March __, 1998 ("Date of
Issuance").

     2.  Exercise.
         ---------

     (a) Manner of Exercise. This Warrant may be exercised, beginning on the
Date of Issuance, as to all or any lesser number of full shares of Common Stock
covered hereby upon surrender of this Warrant, with the Exercise Form attached
as Exhibit A ("Exercise Form") duly executed, together with the full Exercise
Price (as defined in Section 3) for each share of Common Stock as to which this
Warrant is exercised, at the office of the Company, Ancor Communications,
Incorporated, 6130 Blue Circle Drive, Minnetonka, MN 55343; Attention:
President, Telephone No. (612) 932-4000, Facsimile No. (612)

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932-4037, or at such other office or agency as the Company may designate in
writing, by overnight mail, with an advance copy of the Exercise Form by
facsimile (such surrender and payment of the Exercise Price hereinafter called
the "Exercise of this Warrant").

     (b) Date of Exercise. The "Date of Exercise" of the Warrant shall be
defined as the date that the advance copy of the Exercise Form is sent by
facsimile to the Company, provided that the original Warrant, Exercise Form and
full Exercise Price are received by the Company as soon as practicable
thereafter. Alternatively, the Date of Exercise shall be defined as the date the
original Exercise Form is received by the Company, if Holder has not sent
advance notice by facsimile.

     (c) Cancellation of Warrant. This Warrant shall be canceled upon its
Exercise, and, as soon as practical after the Date of Exercise, the Holder
hereof shall be entitled to receive Common Stock certificates representing the
number of shares purchased upon such Exercise, and if this Warrant is not
exercised in full, the Holder shall be entitled to receive a new Warrant or
Warrants (containing terms identical to this Warrant) representing any
unexercised portion of this Warrant in addition to such Common Stock.

     (d) Holder of Record. Each person in whose name any Warrant for shares of
Common Stock is issued shall, for all purposes, be deemed to have become the
Holder of record of such shares on the Date of Exercise of this Warrant,
irrespective of the date of delivery of such shares of Common Stock. Nothing in
this Warrant shall be construed as conferring upon the Holder hereof any rights
as a shareholder of the Company.

     3.  Payment of Warrant Exercise Price.
         ----------------------------------

     The Exercise Price ("Exercise Price") shall equal one hundred fifteen
percent (115%) of the average Closing Bid Price for the five (5) trading days
ending on the date that is one (1) year after the date of the Last Closing of
the Offering (the "One Year Anniversary Date"). As used herein, the terms "Last
Closing" and "Offering" shall have the meanings ascribed to them in the
Regulation D Subscription Agreement entered into between the Company and the
original Holder hereof on or about March 19, 1997 and the term "Closing Bid
Price" shall have the meaning ascribed to it in the Certificate of Designation
of Series B Preferred Stock of Ancor Communications, Incorporated.

     Payment of the Exercise Price shall be made by cash, certified check or
cashiers check or wire transfer.

     4.  Transfer and Registration.
         --------------------------

     (a) Transfer Rights. Subject to the provisions of Section 8 of this
Warrant, this Warrant may be transferred on the books of the Company, in whole
or in part, in person or by attorney, upon surrender of this Warrant properly
endorsed. This Warrant shall be canceled upon such surrender and, as soon as
practicable thereafter, the person to whom such transfer is made shall be
entitled to receive a new Warrant or Warrants as to the 

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portion of this Warrant transferred, and the Holder of this Warrant shall be
entitled to receive a new Warrant or Warrants as to the portion hereof retained.

     (b) Registrable Securities.  The Common Stock issuable upon the exercise of
this Warrant constitute "Registrable Securities" under that certain Registration
Rights Agreement dated on or about March 19, 1997 between the Company and
certain investors and, accordingly, has the benefit of the registration rights
pursuant to that agreement.

     5.  Anti-Dilution Adjustments.
         --------------------------

     (a) Stock Dividend. If the Company shall at any time declare a dividend
payable in shares of Common Stock, then the Holder hereof, upon Exercise of this
Warrant after the record date for the determination of Holders of Common Stock
entitled to receive such dividend, shall be entitled to receive upon Exercise of
this Warrant, in addition to the number of shares of Common Stock as to which
this Warrant is Exercised, such additional shares of Common Stock as such Holder
would have received had this Warrant been Exercised immediately prior to such
record date and the Exercise Price will be proportionately adjusted.

     (b)  Recapitalization or Reclassification. If the Company shall at any
time effect a recapitalization, reclassification or other similar transaction of
such character that the shares of Common Stock shall be changed into or become
exchangeable for a larger or smaller number of shares, then upon the effective
date thereof, the number of shares of Common Stock which the Holder hereof shall
be entitled to purchase upon Exercise of this Warrant shall be increased or
decreased, as the case may be, in direct proportion to the increase or decrease
in the number of shares of Common Stock by reason of such recapitalization,
reclassification or similar transaction, and the Exercise Price shall be, in the
case of an increase in the number of shares, proportionally decreased and, in
the case of decrease in the number of shares, proportionally increased. The
Company shall give the Warrant Holder the same notice it provides to holders of
Common Stock of any transaction described in this Section 5(b).

     (c) Distributions. If the Company shall at any time distribute to Holders
of Common Stock cash, evidences of indebtedness or other securities or assets
(other than cash dividends or distributions payable out of earned surplus or net
profits for the current or preceding year) then, in any such case, the Holder of
this Warrant shall be entitled to receive, upon exercise of this Warrant, with
respect to each share of Common Stock issuable upon such Exercise, the amount of
cash or evidences of indebtedness or other securities or assets which such
Holder would have been entitled to receive with respect to each such share of
Common Stock as a result of the happening of such event had this Warrant been
Exercised immediately prior to the record date or other date fixing shareholders
to be affected by such event (the "Determination Date") or, in lieu thereof, if
the Board of Directors of the Company should so determine at the time of such
distribution, a reduced Exercise Price determined by multiplying the Exercise
Price on the Determination Date by a fraction, the numerator of which is the
result of such

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Exercise Price reduced by the value of such distribution applicable to one share
of Common Stock (such value to be determined by the Board in its discretion) and
the denominator of which is such Exercise Price.

     (d) Notice of Consolidation or Merger. In the event of a merger,
consolidation, exchange of shares, recapitalization, reorganization, or other
similar event, as a result of which shares of Common Stock of the Company shall
be changed into the same or a different number of shares of the same or another
class or classes of stock or securities or other assets of the Company or
another entity or there is a sale of all or substantially all the Company's
assets (a "Corporate Change"), then this Warrant shall be exerciseable into such
class and type of securities or other assets as the Holder would have received
had the Holder exercised this Warrant immediately prior to such Corporate
Change; provided, however, that Company may not affect any Corporate Change
unless it first shall have given thirty (30) business days notice to the Holder
hereof of any Corporate Change.

     (e) Exercise Price Adjusted. As used in this Warrant, the term "Exercise
Price" shall mean the purchase price per share specified in Section 3 of this
Warrant, until the occurrence of an event stated in subsection (a), (b) or (c)
of this Section 5, and thereafter shall mean said price as adjusted from time to
time in accordance with the provisions of said subsection. No such adjustment
under this Section 5 shall be made unless such adjustment would change the
Exercise Price at the time by $.01 or more; provided, however, that all
adjustments not so made shall be deferred and made when the aggregate thereof
would change the Exercise Price at the time by $.01 or more. No adjustment made
pursuant to any provision of this Section 5 shall have the effect of increasing
the Exercise Price. The number of shares of Common Stock subject hereto shall
increase proportionately with each decrease in the Exercise Price.

     (f) Adjustments: Additional Shares, Securities or Assets. In the event that
at any time, as a result of an adjustment made pursuant to this Section 5, the
Holder of this Warrant shall, upon Exercise of this Warrant, become entitled to
receive shares and/or other securities or assets (other than Common Stock) then,
wherever appropriate, all references herein to shares of Common Stock shall be
deemed to refer to and include such shares and/or other securities or assets;
and thereafter the number of such shares and/or other securities or assets shall
be subject to adjustment from time to time in a manner and upon terms as nearly
equivalent as practicable to the provisions of this Section 5.
 
     6.  Fractional Interests.
         ---------------------
 
     No fractional shares or scrip representing fractional shares shall be
issuable upon the Exercise of this Warrant, but on Exercise of this Warrant, the
Holder hereof may purchase only a whole number of shares of Common Stock. If, on
Exercise of this Warrant, the Holder hereof would be entitled to a fractional
share of Common Stock or a right to acquire a fractional share of Common Stock,
such fractional share shall

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be disregarded and the number of shares of Common Stock issuable upon conversion
shall be the next higher number of shares.

     7.   Reservation of Shares.
          ----------------------

          The Company shall at all times reserve for issuance such number of
authorized and unissued shares of Common Stock (or other securities substituted
therefor as herein above provided) as shall be sufficient for Exercise of this
Warrant. The Company covenants and agrees that upon Exercise of this Warrant,
all shares of Common Stock issuable upon such Exercise shall be duly and validly
issued, fully paid, nonassessable and not subject to preemptive rights, rights
of first refusal or similar rights of any person or entity.

     8.   Restrictions on Transfer.
          -------------------------

          (a)  Registration or Exemption Required. This Warrant has been issued
in a transaction exempt from the registration requirements of the Act by virtue
of Regulation D. The Warrant and the Common Stock issuable upon exercise of the
Warrant may not be sold except pursuant to an effective registration statement
or an exemption to the registration requirements of the Act and applicable state
laws.

          (b)  Assignment. Assuming the conditions of (a) above regarding
registration or exemption have been satisfied, the Holder may sell, transfer,
assign, pledge or otherwise dispose of this Warrant, in whole or in part. Holder
shall deliver a written notice to Company, substantially in the form of the
Assignment attached hereto as Exhibit B, indicating the person or persons to
whom the Warrant shall be assigned and the respective number of warrants to be
assigned to each assignee. The Company shall effect the assignment within ten
(10) days, and shall deliver to the assignee(s) designated by Holder a Warrant
or Warrants of like tenor and terms for the appropriate number of shares.

     9.   Benefits of this Warrant.
          -------------------------

          Nothing in this Warrant shall be construed to confer upon any person
other than the Company and the Holder of this Warrant any legal or equitable
right, remedy or claim under this Warrant and this Warrant shall be for the sole
and exclusive benefit of the Company and the Holder of this Warrant.

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     10.  Applicable Law.
          ---------------

          This Warrant is issued under and shall for all purposes be governed by
and construed in accordance with the laws of the state of Minnesota, without
giving effect to conflict of law provisions thereof.
 
     11.  Loss of Warrant.
          ----------------

          Upon receipt by the Company of evidence of the loss, theft,
destruction or mutilation of this Warrant, and (in the case of loss, theft or
destruction) of indemnity or security reasonably satisfactory to the Company,
and upon surrender and cancellation of this Warrant, if mutilated, the Company
shall execute and deliver a new Warrant of like tenor and date.

     12.  Notice or Demands.
          ------------------

Notices or demands pursuant to this Warrant to be given or made by the Holder of
this Warrant to or on the Company shall be sufficiently given or made if sent by
certified or registered mail, return receipt requested, postage prepaid, and
addressed, until another address is designated in writing by the Company, Ancor
Communications, Incorporated, 6130 Blue Circle Drive, Minnetonka, MN 55343,
Attention: President, Telephone No. (612) 932-4059, Facsimile No. (612) 932-
4037. Notices or demands pursuant to this Warrant to be given or made by the
Company to or on the Holder of this Warrant shall be sufficiently given or made
if sent by certified or registered mail, return receipt requested, postage
prepaid, and addressed, to the address of the Holder set forth in the Company's
records, until another address is designated in writing by Holder.


     IN WITNESS WHEREOF, the undersigned has executed this Warrant as of the
______ day of ______, 1998.

                      ANCOR COMMUNICATIONS, INCORPORATED

                                         By: 
                                             -----------------------------------
                                                                               
                                                                    Print Name: 

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

                                      Title: 
                                             -----------------------------------

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                                   EXHIBIT A

                                 EXERCISE FORM

                    TO:  ANCOR COMMUNICATIONS, INCORPORATED

     The undersigned hereby irrevocably exercises the right to purchase
____________ of the shares of Common Stock of ANCOR COMMUNICATIONS,
INCORPORATED, a Minnesota corporation (the "Company"), evidenced by the attached
Warrant, and herewith makes payment of the Exercise Price with respect to such
shares in full, all in accordance with the conditions and provisions of said
Warrant.

1.   The undersigned agrees not to offer, sell, transfer or otherwise dispose of
any of Common Stock obtained on exercise of the Warrant, except in accordance
with the provisions of Section 8(a) of the Warrant.

2.   The undersigned requests that stock certificates for such shares be issued
free of any restrictive legend, and a warrant representing any unexercised
portion hereof be issued, pursuant to the Warrant in the name of the Registered
Holder and delivered to the undersigned at the address set forth below:

Dated:

________________________________________________________________________________
                        Signature of Registered Holder

________________________________________________________________________________
                       Name of Registered Holder (Print)

________________________________________________________________________________
                                    Address

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                                   EXHIBIT B

                                  ASSIGNMENT

                   (To be executed by the registered Holder
                       desiring to transfer the Warrant)

FOR VALUE RECEIVED, the undersigned Holder of the attached Warrant hereby sells,
assigns and transfers unto the person or persons below named the right to
purchase _______ shares of the Common Stock of ANCOR COMMUNICATIONS,
INCORPORATED evidenced by the attached Warrant and does hereby irrevocably
constitute and appoint _______________________ attorney to transfer the said
Warrant on the books of the Company, with full power of substitution in the
premises.

Dated:                          ______________________________
                                          Signature


Fill in for new Registration of Warrant:


-----------------------------------------
                  Name

-----------------------------------------
                  Address

-----------------------------------------
Please print name and address of assignee
(including zip code number)


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NOTICE

The signature to the foregoing Exercise Form or Assignment must correspond to
the name as written upon the face of the attached Warrant in every particular,
without alteration or enlargement or any change whatsoever.

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