Document:

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                                                                   EXHIBIT 10.76

                              SUBSIDIARY GUARANTEE

                                     MADE BY

                             CERTAIN SUBSIDIARIES OF

                            APPLIEDTHEORY CORPORATION

                                   IN FAVOR OF

                          THE LENDERS IDENTIFIED HEREIN

                            DATED AS OF JULY 10, 2001

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                                TABLE OF CONTENTS

SECTION 1. DEFINED TERMS...............................................      1
   1.1     Definitions.................................................      1
   1.2     Other Definitional Provisions...............................      2

SECTION 2. GUARANTEE...................................................      2
   2.1     Guarantee...................................................      2
   2.2     Right Of Contribution.......................................      3
   2.3     No Subrogation..............................................      3
   2.4     Amendments, Etc. With Respect To The Obligations............      3
   2.5     Guarantee Absolute And Unconditional........................      4
   2.6     Reinstatement...............................................      4
   2.7     Payments....................................................      5

SECTION 3. REPRESENTATIONS AND WARRANTIES..............................      5

SECTION 4. COVENANTS...................................................      5

SECTION 5. MISCELLANEOUS...............................................      5
   5.1     Amendments In Writing.......................................      5
   5.2     Notices.....................................................      5
   5.3     No Waiver By Course Of Conduct; Cumulative Remedies.........      5
   5.4     Enforcement Expenses; Indemnification.......................      6
   5.5     Successors And Assigns......................................      6
   5.6     Set-Off.....................................................      6
   5.7     Counterparts................................................      7
   5.8     Severability................................................      7
   5.9     Section Headings............................................      7
   5.10    Integration.................................................      7
   5.11    GOVERNING LAW...............................................      7
   5.12    Submission To Jurisdiction; Waivers.........................      8
   5.13    Acknowledgements............................................      8
   5.14    Additional Guarantors.......................................      8
   5.15    Release Of Guarantors.......................................      9
   5.16    WAIVER OF JURY TRIAL........................................      9

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                  SUBSIDIARY GUARANTEE, dated as of July 10, 2001, made by each
of the signatories hereto (together with any other entity that may become a
party hereto as provided herein, the "GUARANTORS"), in favor of the Lenders as
set forth in, and pursuant to, the Revolving Credit Agreement, dated as of July
10, 2001 (as amended, supplemented or otherwise modified from time to time, the
"LOAN AGREEMENT"), among APPLIEDTHEORY CORPORATION, a Delaware corporation (the
"BORROWER") and the Lenders.

                              W I T N E S S E T H:

                  WHEREAS, pursuant to the Loan Agreement, the Lenders agreed to
make the Loans to the Borrower upon the terms and subject to the conditions set
forth therein;

                  WHEREAS, the Borrower is a member of an affiliated group of
companies that includes each other Guarantor;

                  WHEREAS, the proceeds of the Loans will be used in part to
enable the Borrower to make valuable transfers to one or more of the other
Guarantors in connection with the operation of their respective businesses;

                  WHEREAS, the Borrower and the other Guarantors are engaged in
related businesses, and each Guarantor will derive substantial direct and
indirect benefit from the making of the Loans under the Loan Agreement; and

                  WHEREAS, it is a condition precedent to the obligation of the
Lenders to make the Loans that the Guarantors shall have executed and delivered
this Guarantee to the Lenders;

                  NOW, THEREFORE, in consideration of the premises and to induce
the Lenders to enter into the Loan Agreement and to make the Loans, each
Guarantor hereby agrees with the Lenders as follows:

                            SECTION 1. DEFINED TERMS

                  1.1 Definitions

                  (a) Unless otherwise defined herein, terms defined in the Loan
Agreement and used herein shall have the meanings given to them in the Loan
Agreement.

                  (b) The following terms shall have the following meanings:

                  "GUARANTEE": this Subsidiary Guarantee, as the same may be
amended, supplemented or otherwise modified from time to time.

                  "OBLIGATIONS": the collective reference to the unpaid
principal of and interest on the Loans and all other obligations and liabilities
of the Borrower to the Lenders (including, without limitation, interest accruing
at the then applicable rate provided in the Loan Agreement after the maturity of
the Loans and interest accruing at the then applicable rate provided in the Loan
Agreement after the filing of any petition in bankruptcy, or the commencement of
any insolvency, reorganization or like proceeding, relating to the Borrower, if
a claim for post-filing or post-petition interest is allowed in such proceeding)
whether direct or indirect, absolute or contingent, due or to become due, or now
existing or hereafter incurred, which may arise under,

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out of, or in connection with, the Loan Agreement, this Guarantee or the other
Loan Documents, or any other document made, delivered or given in connection
therewith, in each case whether on account of principal, interest, fees,
indemnities, costs, expenses or otherwise (including, without limitation, all
reasonable fees and disbursements of counsel to the Lenders that are required to
be paid by the Borrower pursuant to the terms of any of the foregoing
agreements).

                  1.2 Other Definitional Provisions

                  (a) The words "hereof," "herein", "hereto" and "hereunder" and
words of similar import when used in this Guarantee shall refer to this
Guarantee as a whole and not to any particular provision of this Guarantee, and
Section and Schedule references are to this Guarantee unless otherwise
specified.

                  (b) The meanings given to terms defined herein shall be
equally applicable to both the singular and plural forms of such terms.

                              SECTION 2. GUARANTEE

                  2.1 Guarantee

                  (a) The Guarantors hereby, jointly and severally,
unconditionally and irrevocably, guarantee to the Lenders and their respective
successors, indorsees, transferees and assigns, the prompt and complete payment
and performance by the Borrower when due (whether at the stated maturity, by
acceleration or otherwise) of the Obligations.

                  (b) Anything herein or in any other Loan Document to the
contrary notwithstanding, the maximum liability of each Guarantor hereunder and
under the other Loan Documents shall in no event exceed the amount which can be
guaranteed by such Guarantor under applicable federal and state laws, including
laws relating to the insolvency of debtors, fraudulent conveyance or transfer or
laws affecting the rights of creditors generally (after giving effect to the
right of contribution established in Section 2.2).

                  (c) Each Guarantor agrees that the Obligations may at any time
and from time to time exceed the amount of the liability of such Guarantor
hereunder without impairing the guarantee contained in this Section 2 or
affecting the rights and remedies of the Lenders hereunder.

                  (d) The guarantee contained in this Section 2 shall remain in
full force and effect until all the Obligations and the obligations of each
Guarantor under the guarantee contained in this Section 2 shall have been
satisfied by payment in full.

                  (e) No payment made by the Borrower, any of the Guarantors,
any other guarantor or any other Person or received or collected by the Lenders
from the Borrower, any of the Guarantors, any other guarantor or any other
Person by virtue of any action or proceeding or any set-off or appropriation or
application at any time or from time to time in reduction of or in payment of
the Obligations shall be deemed to modify, reduce, release or otherwise affect
the liability of any Guarantor hereunder which shall, notwithstanding any such
payment (other than any payment made by such Guarantor in respect of the
Obligations or any payment received or collected from such Guarantor in respect
of the Obligations), remain liable for the Obligations up to the maximum
liability of such Guarantor hereunder until the Obligations are paid in full.

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                  2.2 Right Of Contribution. Each Guarantor hereby agrees that
to the extent that a Guarantor shall have paid more than its proportionate share
of any payment made hereunder, such Guarantor shall be entitled to seek and
receive contribution from and against any other Guarantor hereunder which has
not paid its proportionate share of such payment. Each Guarantor's right of
contribution shall be subject to the terms and conditions of Section 2.3. The
provisions of this Section 2.2 shall in no respect limit the obligations and
liabilities of any Guarantor to the Lenders, and each Guarantor shall remain
liable to the Lenders for the full amount guaranteed by such Guarantor
hereunder.

                  2.3 No Subrogation. Notwithstanding any payment made by any
Guarantor hereunder or any set-off or application of funds of any Guarantor by
the Lenders, no Guarantor shall be entitled to be subrogated to any of the
rights of the Lenders against the Borrower or any other Guarantor or any
collateral security or guarantee or right of offset held by the Lenders for the
payment of the Obligations, nor shall any Guarantor seek or be entitled to seek
any contribution or reimbursement from the Borrower or any other Guarantor in
respect of payments made by such Guarantor hereunder, until all amounts owing to
the Lenders by the Borrower on account of the Obligations are paid in full. If
any amount shall be paid to any Guarantor on account of such subrogation rights
at any time when all of the Obligations shall not have been paid in full, such
amount shall be held by such Guarantor in trust for the Lenders, segregated from
other funds of such Guarantor, and shall, forthwith upon receipt by such
Guarantor, be turned over to the Lenders in the exact form received by such
Guarantor (duly indorsed by such Guarantor to the Lenders, if required), to be
applied against the Obligations, whether matured or unmatured, in such order as
the Lenders may determine.

                  2.4 Amendments, Etc. With Respect To The Obligations. Each
Guarantor shall remain obligated hereunder notwithstanding that, without any
reservation of rights against any Guarantor and without notice to or further
assent by any Guarantor, any demand for payment of any of the Obligations made
by the Lenders may be rescinded by the Lenders and any of the Obligations
continued, and the Obligations, or the liability of any other Person upon or for
any part thereof, or any collateral security or guarantee therefor or right of
offset with respect thereto, may, from time to time, in whole or in part, be
renewed, extended, amended, modified, accelerated, compromised, waived,
surrendered or released by the Lenders, and the Loan Agreement and the other
Loan Documents and any other documents executed and delivered in connection
therewith may be amended, modified, supplemented or terminated, in whole or in
part, as the Lenders may deem advisable from time to time, and any collateral
security, guarantee or right of offset at any time held by the Lenders for the
payment of the Obligations may be sold, exchanged, waived, surrendered or
released. The Lenders shall have no obligation to protect, secure, perfect or
insure any Lien at any time held by them as security for the Obligations or for
the guarantee contained in this Section 2 or any property subject thereto.

                  2.5 Guarantee Absolute And Unconditional. Each Guarantor
waives any and all notice of the creation, renewal, extension or accrual of any
of the Obligations and notice of or proof of reliance by the Lenders upon the
guarantee contained in this Section 2 or acceptance of the guarantee contained
in this Section 2; the Obligations, and any of them, shall conclusively be
deemed to have been created, contracted or incurred, or renewed, extended,
amended or waived, in reliance upon the guarantee contained in this Section 2;
and all dealings between the Borrower and any of the Guarantors, on the one
hand, and the Lenders, on the other hand, likewise shall be

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conclusively presumed to have been had or consummated in reliance upon the
guarantee contained in this Section 2. Each Guarantor waives to the extent
permitted by law diligence, presentment, protest, demand for payment and notice
of default or nonpayment to or upon the Borrower or any of the Guarantors with
respect to the Obligations. Each Guarantor understands and agrees that the
guarantee contained in this Section 2 shall be construed as a continuing,
absolute and unconditional guarantee of payment without regard to (a) the
validity or enforceability of the Loan Agreement or any other Loan Document, any
of the Obligations or any other collateral security therefor or guarantee or
right of offset with respect thereto at any time or from time to time held by
the Lenders, (b) any defense, set-off or counterclaim (other than a defense of
payment or performance) which may at any time be available to or be asserted by
the Borrower or any other Person against the Lenders, or (c) any other
circumstance whatsoever (with or without notice to or knowledge of the Borrower
or such Guarantor) which constitutes, or might be construed to constitute, an
equitable or legal discharge of the Borrower for the Obligations, or of such
Guarantor under the guarantee contained in this Section 2, in bankruptcy or in
any other instance. When making any demand hereunder or otherwise pursuing its
rights and remedies hereunder against any Guarantor, the Lenders may, but shall
be under no obligation to, make a similar demand on or otherwise pursue such
rights and remedies as they may have against the Borrower, any other Guarantor
or any other Person or against any collateral security or guarantee for the
Obligations or any right of offset with respect thereto, and any failure by the
Lenders to make any such demand, to pursue such other rights or remedies or to
collect any payments from the Borrower, any other Guarantor or any other Person
or to realize upon any such collateral security or guarantee or to exercise any
such right of offset, or any release of the Borrower, any other Guarantor or any
other Person or any such collateral security, guarantee or right of offset,
shall not relieve any Guarantor of any obligation or liability hereunder, and
shall not impair or affect the rights and remedies, whether express, implied or
available as a matter of law, of the Lenders against any Guarantor. For the
purposes hereof, "demand" shall include the commencement and continuance of any
legal proceedings.

                  2.6 Reinstatement. The guarantee contained in this Section 2
shall continue to be effective, or be reinstated, as the case may be, if at
anytime payment, or any part thereof, of any of the Obligations is rescinded or
must otherwise be restored or returned by the Lenders upon the insolvency,
bankruptcy, dissolution, liquidation or reorganization of the Borrower or any
Guarantor, or upon or as a result of the appointment of a receiver, intervenor
or conservator of, or trustee or similar officer for, the Borrower or any
Guarantor or any substantial part of its property, or otherwise, all as though
such payments had not been made.

                  2.7 Payments. Each Guarantor hereby guarantees that payments
hereunder will be paid to the Lenders without set-off or counterclaim in U.S.
dollars at the address set forth or referred to in Section 11.1 of the Loan
Agreement.

                   SECTION 3. REPRESENTATIONS AND WARRANTIES

                  To induce the Lenders to enter into the Loan Agreement and to
make the Loans thereunder, each Guarantor hereby represents and warrants to the
Lenders that the representations and warranties set forth in Section 4 of the
Loan Agreement as they relate to such Guarantor or to the Loan Documents to
which such Guarantor is a party, each of which is hereby incorporated herein by
reference, are true and correct as of each time such representations are

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deemed to be made pursuant to such Article 4, and the Lenders shall be entitled
to rely on each of them as if they were fully set forth herein, PROVIDED that
each reference in each such representation and warranty to the Borrower's
knowledge shall, for the purposes of this Section 3, be deemed to be a reference
to such Guarantor's knowledge.

                              SECTION 4. COVENANTS

                  Each Guarantor covenants and agrees with the Lenders that,
from and after the date of this Guarantee until the Obligations shall have been
paid in full, such Guarantor (x) shall take, and/or shall refrain from taking,
as the case may be, each commercially reasonable action that is necessary to be
taken or not taken, as the case may be, so that no Default or Event of Default
is caused by the failure to take such action or to refrain from taking such
action by such Guarantor and (y) without limitation, shall take, and/or refrain
from taking, as the case may be, all actions so that all covenants in Articles 6
and 7 of the Loan Agreements are performed in accordance with their terms.

                            SECTION 5. MISCELLANEOUS

                  5.1 Amendments In Writing. None of the terms or provisions of
this Guarantee may be waived, amended, supplemented or otherwise modified except
in accordance with Section 11.6 of the Loan Agreement.

                  5.2 Notices. All notices, requests and demands to or upon the
Lenders or any Guarantor hereunder shall be effected in the manner provided for
in Section 11.1 of the Loan Agreement; PROVIDED that any such notice, request or
demand to or upon any Guarantor shall be addressed to such Guarantor at its
notice address set forth on SCHEDULE 1.

                  5.3 No Waiver By Course Of Conduct; Cumulative Remedies. The
Lenders shall not by any act (except by a written instrument pursuant to Section
5.1), delay, indulgence, omission or otherwise be deemed to have waived any
right or remedy hereunder or to have acquiesced in any Default or Event of
Default. No failure to exercise, nor any delay in exercising, on the part of the
Lenders, any right, power or privilege hereunder shall operate as a waiver
thereof. No single or partial exercise of any right, power or privilege
hereunder shall preclude any other or further exercise thereof or the exercise
of any other right, power or privilege. A waiver by the Lenders of any right or
remedy hereunder on any one occasion shall not be construed as a bar to any
right or remedy which the Lenders would otherwise have on any future occasion.
The rights and remedies herein provided are cumulative, may be exercised singly
or concurrently and are not exclusive of any other rights or remedies provided
by law.

                  5.4 Enforcement Expenses; Indemnification

                  (a) Each Guarantor agrees to pay, or reimburse the Lenders
for, all its costs and expenses incurred in collecting against such Guarantor
under the guarantee contained in Section 2 or otherwise enforcing or preserving
any rights under this Guarantee and the other Loan Documents to which such
Guarantor is a party, including, without limitation, the reasonable fees and
disbursements of counsel to the Lenders.

                  (b) Each Guarantor agrees to pay, and to save the Lenders
harmless from, any and all liabilities with respect to, or resulting from any
delay in paying, any and all stamp, excise,

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sales or other taxes which may be payable or determined to be payable in
connection with any of the transactions contemplated by this Guarantee.

                  (c) Each Guarantor agrees to pay, and to save the Lenders
harmless from, any and all liabilities, obligations, losses, damages, penalties,
actions, judgments, suits, costs, expenses or disbursements of any kind or
nature whatsoever with respect to the execution, delivery, enforcement,
performance and administration of this Guarantee to the extent the Borrower
would be required to do so pursuant to the Loan Agreement.

                  (d) The agreements in this Section shall survive repayment of
the Obligations and all other amounts payable under the Loan Agreement and the
other Loan Documents.

                  5.5 Successors And Assigns. This Guarantee shall be binding
upon the successors and assigns of each Guarantor and shall inure to the benefit
of the Lenders and their respective successors and assigns; PROVIDED that no
Guarantor may assign, transfer or delegate any of its rights or obligations
under this Guarantee without the prior written consent of the Lenders.

                  5.6 Set-Off. Each Guarantor hereby irrevocably authorizes the
Lenders at any time and from time to time while an Event of Default shall have
occurred and be continuing, without notice to such Guarantor or any other
Guarantor, any such notice being expressly waived by each Guarantor, to set-off
and appropriate and apply any and all deposits (general or special, time or
demand, provisional or final), in any currency, and any other credits,
indebtedness or claims, in any currency, in each case whether direct or
indirect, absolute or contingent, matured or unmatured, at any time held or
owing by the Lenders to or for the credit or the account of such Guarantor, or
any part thereof in such amounts as the Lenders may elect, against and on
account of the obligations and liabilities of such Guarantor to the Lenders
hereunder and claims of every nature and description of the Lenders against such
Guarantor, in any currency, whether arising hereunder, under the Loan Agreement,
any other Loan Document or otherwise, as the Lenders may elect, whether or not
the Lenders have made any demand for payment and although such obligations,
liabilities and claims may be contingent or unmatured. The Lenders shall notify
such Guarantor promptly of any such set-off and the application made by the
Lenders of the proceeds thereof, PROVIDED that the failure to give such notice
shall not affect the validity of such set-off and application. The rights of the
Lenders under this Section are in addition to other rights and remedies
(including, without limitation, other rights of set-off) which the Lenders may
have.

                  5.7 Counterparts. This Guarantee may be executed by one or
more of the parties to this Guarantee on any number of separate counterparts
(including by telecopy), and all of said counterparts taken together shall be
deemed to constitute one and the same instrument.

                  5.8 Severability. Any provision of this Guarantee which is
prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction,
be ineffective to the extent of such prohibition or unenforceability without
invalidating the remaining provisions hereof, and any such prohibition or
unenforceability in any jurisdiction shall not invalidate or render
unenforceable such provision in any other jurisdiction.

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                  5.9 Section Headings. The Section headings used in this
Guarantee are for convenience of reference only and are not to affect the
construction hereof or be taken into consideration in the interpretation hereof.

                  5.10 Integration. This Guarantee and the other Loan Documents
represent the agreement of the Guarantors and the Lenders with respect to the
subject matter hereof and thereof, and there are no promises, undertakings,
representations or warranties by the Lenders relative to subject matter hereof
and thereof not expressly set forth or referred to herein or in the other Loan
Documents.

                  5.11 GOVERNING LAW. THIS GUARANTEE SHALL BE GOVERNED BY, AND
CONSTRUED AND INTERPRETED IN ACCORDANCE WITH, THE LAW OF THE STATE OF NEW YORK.

                  5.12 Submission To Jurisdiction; Waivers. Each Guarantor
hereby irrevocably and unconditionally:

                  (a) submits for itself and its property in any legal action or
proceeding relating to this Guarantee and the other Loan Documents to which it
is a party, or for recognition and enforcement of any judgment in respect
thereof, to the non-exclusive general jurisdiction of the Courts of the State of
New York, located in New York County, New York, the courts of the United States
of America for the Southern District of New York, and appellate courts from any
thereof;

                  (b) consents that any such action or proceeding may be brought
in such courts and waives any objection that it may now or hereafter have to the
venue of any such action or proceeding in any such court or that such action or
proceeding was brought in an inconvenient court and agrees not to plead or claim
the same;

                  (c) agrees that service of process in any such action or
proceeding may be effected by mailing a copy thereof by registered or certified
mail (or any substantially similar form of mail), postage prepaid, to such
Guarantor at its address referred to in Section 5.2 or at such other address of
which the Lenders shall have been notified pursuant thereto;

                  (d) agrees that nothing herein shall affect the right to
effect service of process in any other manner permitted by law or shall limit
the right to sue in any other jurisdiction; and

                  (e) waives, to the maximum extent not prohibited by law, any
right it may have to claim or recover in any legal action or proceeding referred
to in this Section any special, exemplary, punitive or consequential damages.

                  5.13 Acknowledgements. Each Guarantor hereby acknowledges
that:

                  (a) it has been advised by counsel in the negotiation,
execution and delivery of this Guarantee and the other Loan Documents to which
it is a party;

                  (b) the Lenders have no fiduciary relationship with or duty to
any Guarantor arising out of or in connection with this Guarantee or any of the
other Loan Documents, and the

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relationship between the Guarantors, on the one hand, and the Lenders, on the
other hand, in connection herewith or therewith is solely that of debtor and
creditor; and

                  (c) no joint venture is created hereby or by the other Loan
Documents or otherwise exists by virtue of the transactions contemplated hereby
among the Guarantors and the Lenders.

                  5.14 Additional GuarantorsThe Company shall cause each of its
subsidiaries formed or acquired on or subsequent to the date hereof, other than
an inactive subsidiary having less than $1,000 in assets, to become a Guarantor
for all purposes of this Guarantee by executing and delivering an Assumption
Agreement in the form of Annex 1 hereto.

                  5.15 Release Of Guarantors

                  Subject to Section 2.6, each Guarantor will be released from
all liability hereunder concurrently with the repayment in full of all amounts
owed under the Loan Agreement and the Loans.

                  5.16 WAIVER OF JURY TRIAL. EACH GUARANTOR AND, BY ACCEPTANCE
OF THE BENEFITS HEREOF, EACH LENDER, HEREBY IRREVOCABLY AND UNCONDITIONALLY
WAIVES TRIAL BY JURY IN ANY LEGAL ACTION OR PROCEEDING RELATING TO THIS
GUARANTEE AND FOR ANY COUNTERCLAIM THEREIN.

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                  IN WITNESS WHEREOF, each of the undersigned has caused this
Guarantee to be duly executed and delivered as of the date first above written.

                                      GUARANTORS:

                                      APPLIEDTHEORY GEORGIA CORPORATION

                                      By:      /s/ Danny E. Stroud
                                         ---------------------------------------
                                               Danny E. Stroud, President

                                      APPLIEDTHEORY SEATTLE CORPORATION

                                      By:      /s/ Danny E. Stroud
                                         ---------------------------------------
                                               Danny E. Stroud, President

                                      APPLIEDTHEORY CALIFORNIA CORPORATION

                                      By:      /s/ Danny E. Stroud
                                         ---------------------------------------
                                               Danny E. Stroud, President

                                      APPLIEDTHEORY VIRGINIA CORPORATION

                                      By:      /s/ Danny E. Stroud
                                         ---------------------------------------
                                               Danny E. Stroud, President

                                      APPLIEDTHEORY AUSTIN CORPORATION

                                      By:      /s/ Danny E. Stroud
                                         ---------------------------------------
                                               Danny E. Stroud, President

                                      APPLIEDTHEORY COLORADO CORPORATION

                                      By:      /s/ Danny E. Stroud
                                         ---------------------------------------
                                               Danny E. Stroud, President<PAGE>   1
                                                                   EXHIBIT 10.77

July 10, 2001

AppliedTheory Corporation
224 Harrison Street, 8th Floor
Syracuse, New York  13202

         I. Reference is made to the documents being entered into today by
AppliedTheory Corporation (the "Company"); its subsidiaries (the "Subsidiaries")
and the undersigned Lenders ("Lenders"), in connection with the "Current
Indebtedness" and "Receivables Financing" as such terms are defined in the
Security Agreement dated today among the Company, the Subsidiaries, the Lenders
and the Collateral Agent thereunder. Other terms used in this Part I and not
defined have the same meanings as in the Security Agreement.

         (A) Notwithstanding anything to the contrary in the documents
comprising the Current Indebtedness and Receivables Financing, the following two
actions (referred to below as the "Specified Actions") will not by themselves
constitute an Event of Default under any such documents; provided that (a) at
such time or times there is otherwise no Default or Event of Default existing
under the Security Agreement, (b) with respect to any claims, damages or
penalties of James G. Couch, a former shareholder of CRL Network Services, Inc.
("Couch") against the Company and the Subsidiaries under the Put Option
Agreement dated as of January 5, 2000 among the Company, Couch and other former
shareholders of CRL Network Services, Inc., such actions result in a full and
complete settlement of any and all claims as evidenced by a release, in form and
substance satisfactory to the Lenders, (c) with respect to any claims (including
governmental claims, fines and penalties) against the Company in connection with
services rendered to NYSERNet.net, such actions will result in a full and
complete settlement of all civil claims, and at the time of such actions there
shall not be pending or overtly threatened any criminal claims against the
Company or its subsidiaries arising from services rendered to NYSERNet.net
(collectively, the "NYSERNET Claims") as evidenced by a release and/or other
documentation, in form and substance satisfactory to the Lenders, (d) such
actions will not violate any applicable federal or state laws, (e) such actions
will not result in a diminution of Lenders' rights under the Current
Indebtedness or Receivables Financing pursuant to any laws relating to the
insolvency of debtors, fraudulent conveyance or transfer, or laws affecting the
rights of Creditors generally and (f) the Company shall deliver to the Lenders a
favorable
<PAGE>   2
opinion of outside counsel, reasonably satisfactory to the Lenders with respect
to the matters covered by (c), (d) and (e) above:

         The Specified Actions

         1.       The payment by the Company of not more than $1,000,000 in cash
                  collectively to both Couch and/or any claimants (including
                  governmental entities) in connection with the NYSERNET Claims;
                  and

         2.       The grant by the Company of a lien in certain Collateral under
                  the Security Agreement to Couch to the extent permitted under
                  Section 2.2(e)(ii) of the Security Agreement (as supplemented
                  by this letter) to secure payment of the balance of any amount
                  agreed to be paid to Couch in settlement of his claims and/or
                  as the price for the redemption of Couch's shares of the
                  capital stock of the Company; provided that any payments to
                  Couch with respect to such balance shall not be due or
                  actually paid until at least three months after the later of
                  (i) the final maturity of the Debentures and (ii) the
                  Revolving Credit Termination Date; and provided further that
                  Couch enters into an intercreditor agreement with the Lenders
                  in form and substance reasonably satisfactory to the Lenders.

         For the avoidance of doubt, it is hereby agreed that (i) the payment by
the Obligors of more than $1,000,000 in the aggregate (A) to Couch, and/or (B)
to any other person in respect of the NYSERNET Claims or (ii) the grant by the
Company of any security interest in any assets of the Company or any of its
subsidiaries in connection with the NYSERNET Claims, will constitute an Event of
Default under the Revolving Credit Agreement, the Security Agreement and the
Debentures. The parties also acknowledge and agree that (i) the reference to
stayed attachments or judgement Liens in Section 7.1(9) of the Revolving Credit
Agreement and (ii) the reference in Section 14(i) of the Amendment Agreement to
pending litigation disclosed in the Pre-Closing SEC Documents, shall be deemed
to refer only to the litigation, judgements and attachments arising out of the
claims made by Couch and the NYSERNET Claims.

         (B) Except as otherwise permitted under Section 2.2(e)(i) of the
Security Agreement or except for a Relevant Sale (as defined in the Amendment
Agreement), the Company and each of the Subsidiaries covenant that as long as
any Amended Debenture, Participation Certificate or Revolving Credit Note is
outstanding, neither the Company nor any Subsidiary shall enter into any
agreement outside its ordinary course of business (such ordinary course of
business being consistent with past business practices) without the express
prior written consent of the Lenders. The exclusion of a Relevant Sale from the
requirement of prior written consent is not intended to eliminate the existence
of an Event of Default that would otherwise occur under the Revolving Credit
Agreement as a result of the Relevant Sale.

         II. Reference is further made to the Amendment Agreement and the
Purchase Agreement referred to in the Security Agreement: for the purposes of
this Part II, capitalized terms which are not defined shall have the meanings
set forth in the Amendment Agreement or the Purchase Agreement.

                                       2
<PAGE>   3
         (A)(1) If and only if the SEC takes the position that, solely as a
result of the Company's execution and delivery of the July 2001 Transaction
Documents, the Company is required to file a post-effective amendment pursuant
to Item 512(a)(1)(iii) of Regulation S-K (the "SEC Position"), then the Company
shall deliver to the Investors and file with the SEC a post-effective amendment
to the Registration Statement in accordance with the rules and regulations under
the Security Act. Any such post-effective amendment (a) shall be filed with the
SEC within 15 days of the Company's first receipt of notice of the SEC's
position ("SEC Notice Date") and (b) shall be submitted to the Investors at
least two (2) Trading Days prior to its filing for review and (c) shall be
subject to the Investors' prior approval, which shall not be unreasonably
withheld or delayed. The Company shall use its best efforts (i) to cause any
such post-effective amendment, when filed, to become effective under the
Securities Act within 60 days of the SEC Notice Date and (ii) keep such
post-effective amendment effective during the period described in Section 5 of
the Registration Rights Agreement. All of the registration rights and remedies
under the Registration Rights Agreement shall apply to the post-effective
amendment and the Registrable Securities registered thereunder (including
without limitation the provisions providing for Default Payments and Premium
Redemption Price) except that references in the Registration Rights Agreement to
April 11, 2001 shall be deemed to refer to the 60th day following the SEC Notice
Date and references to June 11, 2001 shall be deemed to refer to the 75th day
date following the SEC Notice Date. The Company shall immediately notify in
writing (i) the Investors of the date on which the post-effective amendment has
been filed and the date on which the post-effective amendment has become
effective (notification of such filing and effectiveness shall be delivered to
the Investors by facsimile on the same day of such filing or effectiveness and
by overnight mail) and (ii) the Investors' Counsel of any request by the SEC for
additional information. Reference is also made to Section 2(b)(iii) of the
Registration Rights Agreement. Provided that a Blackout (as defined in the
Registration Rights Agreement) is triggered solely as a result of the SEC taking
the SEC Position, the Company shall be entitled to a Suspension Grace Period
that will commence on the SEC Notice Date (if any) and expire on the earlier of
(x) the sixtieth (60th) day thereafter and (y) the effective date of the
post-effective amendment. This Suspension Grace Period, if utilized, will
replace the Suspension Grace Period set forth in Section 2(b)(iii) of the
Registration Rights Agreement (which will no longer apply).

         (2) In the event that Section 3(b) of the Amendment Agreement is not
true solely as a result of the SEC Position, then no Event of Default shall have
occurred under such Section 3(b). Notwithstanding the preceding sentence, in the
event that Section 3(b) of the Amendment Agreement is not true the Company must
indemnify each of the Investors, each of its officers, directors and partners,
and each person controlling each Investor, within the meaning of Section 15 of
the Securities Act for any loss, expense or damage arising as a result of
Section 3(b) not being true, and shall reimburse each Investor, each of its
officers, directors and partners, and each person controlling such Investor for
any legal and any other expenses reasonably incurred in connection with
investigating and defending any such claim, loss, damage, expense, liability or
action.

         (B) In addition to the other criteria which define Marketable
Securities for purposes of determining whether a Sale of the Company is a
Relevant Sale under the terms of Section 2(c) of the Amendment Agreement, a
Relevant Sale must also satisfy the following (in addition to the criteria set
forth in said Section 2(c)): (i) the amount of the value of the Marketable
Securities received by the Investors that comprises the Relevant Sale
Consideration shall not exceed 30%

                                       3
<PAGE>   4
of the Total Dollar Volume (as defined below) of the Marketable Securities for
the 40 Trading Days prior to the date of the announcement of the Relevant Sale;
and (ii) the amount of the value of the Marketable Securities received by the
Investors that comprises the Relevant Sale Consideration shall not exceed 10% of
the Total Dollar Volume of the Marketable Securities during the six (6) month
period prior to the date of the announcement of the Relevant Sale. For purposes
of this Section II(B), "Total Dollar Volume" shall mean the sum of the product,
for each Trading Day during the period (40 Trading Days or 6 months, as
applicable) of the VWAP for such Trading Day multiplied by the total number of
shares of common stock traded on the principal market for such shares during
that Trading Day. For purposes of this Section II(B), trades of greater than
20,000 shares of common stock shall be excluded from the computation of Total
Dollar Volume. Marketable Securities shall be valued as set forth in Section
2(c) of the Amendment Agreement.

                                       4
<PAGE>   5
                                 LENDERS:

                                 HALIFAX FUND, L.P.
                                 By:      THE PALLADIN GROUP, L.P.
                                          Attorney-in-Fact

                                 By:       /s/ Maurice Hryshko
                                          --------------------------------------
                                          Name:  Maurice Hryshko
                                          Title:  Counsel

                                 PALLADIN PARTNERS I, L.P.
                                 By:      THE PALLADIN GROUP, L.P.
                                           Attorney-in-Fact

                                 By:       /s/ Maurice Hryshko
                                          --------------------------------------
                                          Name:  Maurice Hryshko
                                          Title:  Counsel

                                 PALLADIN OVERSEAS FUND LTD.
                                 By:        THE PALLADIN GROUP, L.P.
                                            Attorney-in-Fact

                                 By:       /s/ Maurice Hryshko
                                          --------------------------------------
                                          Name:  Maurice Hryshko
                                          Title:  Counsel

                                 DEAM CONVERTIBLE ARBITRAGE FUND, LTD.

                                 By:       /s/ Maurice Hryshko
                                          --------------------------------------
                                          Name:  Maurice Hryshko
                                          Title:  Counsel

                                 LANCER SECURITIES (CAYMAN) LTD.
                                 By:        THE PALLADIN GROUP, L.P.
                                            Attorney-in-Fact

                                 By:       /s/ Maurice Hryshko
                                          --------------------------------------
                                          Name:  Maurice Hryshko
                                          Title:  Counsel
<PAGE>   6
                                 ELLIOTT ASSOCIATES, L.P.

                                 By:       /s/ Paul E. Singer
                                          --------------------------------------
                                          Name:  Paul E. Singer
                                          Title:  General Partner

                                 ELLIOTT INTERNATIONAL, L.P.
                                 By:        ELLIOTT INTERNATIONAL CAPITAL
                                            ADVISORS INC.
                                            Attorney-in-Fact

                                 By:        s/ Paul E. Singer
                                          --------------------------------------
                                          Name: Paul E. Singer
                                          Title:  President
Agreed and Accepted

APPLIEDTHEORY CORPORATION

By:      /s/ Danny E. Stroud
   ----------------------------------------
         Danny E. Stroud, President

APPLIEDTHEORY GEORGIA CORPORATION

By:      /s/ Danny E. Stroud
   ----------------------------------------
         Danny E. Stroud, President

APPLIEDTHEORY SEATTLE CORPORATION

By:      /s/ Danny E. Stroud
   ----------------------------------------
         Danny E. Stroud, President

APPLIEDTHEORY CALIFORNIA CORPORATION

By:      /s/ Danny E. Stroud
   ----------------------------------------
         Danny E. Stroud, President
<PAGE>   7
APPLIEDTHEORY VIRGINIA CORPORATION

By:      /s/ Danny E. Stroud
   -----------------------------------------
         Danny E. Stroud, President

APPLIEDTHEORY AUSTIN CORPORATION

By:      /s/ Danny E. Stroud
   -----------------------------------------
         Danny E. Stroud, President

APPLIEDTHEORY COLORADO CORPORATION

By:      /s/ Danny E. Stroud
   -----------------------------------------
         Danny E. Stroud, President

                         [SIGNATURE PAGE TO SIDE LETTER]

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