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                                                                   EXHIBIT 10.73

                            PARTICIPATION CERTIFICATE

         This PARTICIPATION CERTIFICATE is delivered by AppliedTheory
Corporation, a Delaware corporation (the "Company"), to ____________, a
_________ [TYPE AND JURISDICTION OF ENTITY] (the "PARTICIPANT"), pursuant to
that certain Amendment Agreement (the "AMENDMENT AGREEMENT") between the Company
and the Participant, among other Investors, dated the date hereof. Capitalized
terms which are not defined herein shall have the meaning set forth in the
Amendment Agreement. In connection therewith, the Company hereby certifies to
the Participant as follows:

         1. The Company hereby irrevocably participates and transfers to
Participant the right to receive certain percentages of the consideration (such
percentages of the consideration shall hereinafter be referred to as the
"PARTICIPANT'S INTEREST" and, together with the other rights of the Participant
hereunder, as the "PARTICIPATION") otherwise paid and payable, directly or
indirectly, to the Company, its subsidiaries, its shareholders, its affiliates
or any other person on behalf of the Company (each, a "PAYEE") by or on behalf
of any acquirer in connection with each Sale of the Company up to and including
the earlier of the Last Sale Date and the date of a Relevant Sale, as set forth
below:

         a. [___]% of the consideration up to $10,000,000 shall be paid to the
Participant.

         b. [___]% of the consideration between $10,000,000 and $30,000,000
shall be paid to the Participant.

         c. [____]% of the consideration between $30,000,000 and $50,000,000
shall be paid to the Participant.

         d. [___]% of the consideration above $50,000,000 shall be paid to the
Participant.

         For the avoidance of doubt, in a case where a Sale of the Company
resulted in consideration of $10,000,000, then, with respect to the next Sale of
the Company, the schedule would commence with paragraph (b) above.

         2. The Company represents and warrants to the Participant as of the
date hereof that this Certificate has been duly and validly authorized, executed
and delivered by the Company and is legal, valid, binding and enforceable
against the Company in accordance with its terms.

         3. The Company has not, directly or indirectly, assigned, transferred,
participated, sold, conveyed, disposed of or terminated, in whole or in part,
any of its right, title and interest in and to the Participated Interest, except
to the other Investors in accordance with the Amendment Agreement and the
participation certificates issued in connection therewith, and is not a party to
any other agreement or obligation which would result in any of the foregoing.
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         4. Neither the execution, delivery and performance of this Certificate,
nor this transfer of the Participation by the Company, has resulted, or will
result, in any breach of any provision of, or constitute a default (or an event
which with or without notice and/or lapse of time would constitute a default)
under any agreement or instrument to which the Company is a party or by which it
is bound, or any statute, order, rule or regulation applicable to it of any
court or other governmental agency.

         5. The Company agrees not to sell, assign, divide, subparticipate,
pledge, or otherwise transfer or encumber the Participation, the Participated
Interest, or any portion thereof or interest therein, and agrees to take all
steps necessary to ensure that no other Payee takes any such action, without the
prior written consent of the Participant.

         6. Whenever a Payee is to receive or collect any consideration pursuant
to a Sale of the Company, the Company shall take all steps necessary to ensure
that the Participant's Interests in such cash or other payment or property is
paid to Participant on the Payment Date. If any payments or distributions made,
or caused to be made, by the Company to Participant hereunder are made in error
or are otherwise required to be returned or disgorged by the Company for any
reason, Participant shall immediately return such payments and distributions to
the Company.

         7. Payments and deliveries to the Company or Participant in connection
with this Certificate shall be made as may be reasonably directed in writing by
Participant or the Company, as applicable.

         8. Nothing herein shall be deemed to limit the rights of the
Participant as Investor under the Amendment Agreement.

         9. Article 6 of the Purchase Agreement (except for Section 6.5 thereof)
is hereby incorporated herein by reference and shall apply to this Participation
Certificate with such changes as may be necessary mutatis mutandis to conform to
this Participation Certificate.

         10. The Company agrees that the Participant may rely upon the
representations of Company contained herein.


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                  Dated:            July __, 2001

                                       APPLIEDTHEORY CORPORATION

                                       By:______________________________________
                                            Name:  Danny Stroud
                                            Title:    Chief Executive Officer

ACCEPTED AND ACKNOWLEDGED:

By:      ________________________
         Name:
         Title:


                  [SIGNATURE PAGE TO PARTICIPATION CERTIFICATE]