<PAGE>
                                                                   EXHIBIT 10.78

            AMENDMENT NO. 1 dated as of October 10, 2001 to (i) the Revolving
Credit Agreement dated as of July 10, 2001 (the "Credit Agreement"), among
AppliedTheory Corporation, a Delaware corporation (the "Borrower"), the
subsidiaries of the Borrower listed on Exhibit D to the Credit Agreement (the
"Subsidiaries") and the various financial institutions parties thereto (the
"Lenders") and (ii) the Security Agreement, dated as of July 10, 2001 (the
"Security Agreement") among the Borrower, the Subsidiaries, the Lenders and
Halifax Fund, L.P. as collateral agent (this "Amendment").

                              W I T N E S S E T H :

            WHEREAS, capitalized terms used herein and not otherwise defined
herein shall have the meanings assigned to such terms in the Credit Agreement;
and

            WHEREAS, the Loan Obligors and the Lenders have entered into the
Credit Agreement and the Security Agreement; and

            WHEREAS, the Loan Obligors and the Lenders are willing, on the terms
and subject to the conditions set forth below, to amend certain provisions of
the Credit Agreement (the Credit Agreement, after giving effect to the
amendments contained herein, being referred to as the "Amended Credit
Agreement") and the Security Agreement (the Security Agreement, after giving
effect to the amendments contained herein, being referred to as the "Amended
Security Agreement");

            NOW THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, and in consideration of the
agreements herein, the parties hereto agree as follows:

                                   ARTICLE I.

                           CREDIT AGREEMENT AMENDMENTS

            SECTION 1.1. Definitions; References. Unless otherwise specifically
defined herein, each term used herein which is defined in the Credit Agreement
shall have the meaning assigned to such term in the Credit Agreement.

            SECTION 1.2. Effectiveness. The Loan Obligors and the Lenders
severally agree that the following amendments and waivers in this Article I to
the Credit Agreement shall become effective on the Amendment Effective Date (as
defined below).

            SECTION 1.3. Amendments to Recitals The recital is amended by
deleting the term "$6 million" in the first sentence thereof and replacing it
with "$7 million."

            SECTION 1.4. Amendments to Section 1.1 Section 1.1 of the Credit
Agreement is amended by deleting the definition of "Total Revolving Credit
Commitment" in its entirety and by substituting in lieu thereof the following:
<PAGE>
            "Total Revolving Credit Commitment" shall mean the total of each
Lender's Revolving Credit Commitments, which in the aggregate as to all Lenders
(subject to reduction after each anniversary date of this Agreement) shall equal
$7 million."

            SECTION 1.5. Amendments to Section 6 Section 6 of the Credit
Agreement is amended by adding at the end thereof the following:

            "Section 6.10 Daily Reports Furnish the Lenders with daily cash
reports setting forth in detail the prior day's cash disbursements, receipts and
balances."

            SECTION 1.6. Amendments to Exhibit A. Exhibit A is amended and
restated in its entirety to read as follows:

                      LENDERS' REVOLVING CREDIT COMMITMENTS

<TABLE>
<CAPTION>
               LENDER                                REVOLVING CREDIT COMMITMENT
               ------                                ---------------------------
<S>                                                  <C>
Halifax Fund, L.P.                                           3,658,536
Palladin Partners I, L.P.                                      292,684
Palladin Overseas Fund Ltd.                                    365,855
DeAM Convertible Arbitrage Fund, Ltd.                          658,532
Lancer Securities (Cayman) Ltd.                                512,197
Elliott Associates, L.P.                                       680,491
Elliott International, L.P.                                    831,705
</TABLE>


            SECTION 1.7. Waiver of Compliance with Section 5.1(5) and
5.1(7)(ii). The Lenders hereby waive any noncompliance by the Borrower with the
provisions of Section 5.1(5) and Section 5.1(7)(ii) of the Credit Agreement
solely in connection with the $2,871,970 funded by the Lenders on the Amendment
Effective Date. The Loan Obligors hereby expressly acknowledge that as a result
of the extension of credit on the Amendment Effective Date an Event of Default
shall exist and be continuing under the Credit Agreement and the Security
Agreement. The Loan Obligors further acknowledge that the Lenders are not
waiving any Event of Default or any other section or provision of the Credit
Agreement or Loan Documents, including but not limited to Section 6.5. of the
Credit Agreement and such provisions shall remain in full force and effect as
set forth in Section 5.1 hereto.

                                  ARTICLE II.

                          SECURITY AGREEMENT AMENDMENTS


                                       2
<PAGE>
            SECTION 2.1. References. Unless specifically defined in Article II,
each term used in Article II which is defined in the Security Agreement shall
have the meaning assigned to such term in the Security Agreement.

            SECTION 2.2. Effectiveness. The Loan Obligors and the Lenders agree
that the following amendments and waivers in this Article II to the Security
Agreement shall become effective on the Amendment Effective Date (as defined
below).

            SECTION 2.3. Recitals. The sixth Whereas clause is hereby amended
and restated in its entirety to read as follows:

            "WHEREAS, pursuant to the terms of a Revolving Credit Agreement,
dated as of July 10, 2001, by and between the Obligors and the Lenders as
amended, supplemented or otherwise modified from time to time (the "Revolving
Credit Agreement") and the Revolving Credit Notes, as amended, supplemented or
otherwise modified from time to time issued thereunder (the "Revolving Credit
Notes"), the financing provided thereunder to the Obligors, together with all
obligations of the Obligors and the Lenders thereunder and under the Subsidiary
Guarantees (the "Subsidiary Guarantees") delivered by each of the Subsidiaries
and the Parent Guarantee (the "Parent Guarantee") delivered by the Borrower (the
"Receivables Financing," and together with the "Current Indebtedness, the
"Indebtedness") shall be secured by a first priority lien (except as provided
herein) on certain assets of the Obligors, pursuant to this Agreement."

            SECTION 2.4. Definitions.

            The definition of "Collateral" is hereby amended to add the
following after the term "the Pledged Securities;"

            "commercial tort claims; investment property; letter of credit
rights;"

                                  ARTICLE III.

                   AMENDMENT FEE; CONDITIONS TO EFFECTIVENESS

            SECTION 3.1. Amendment Effective Date. This Amendment, and the
waivers and amendments contained herein shall be and become effective on the
date (the "Amendment Effective Date") when each of the conditions set forth in
this Article III shall have been fulfilled to the satisfaction of the Lenders:

            (a) Revolving Credit Notes. The Lenders shall have received amended
Revolving Credit Notes in the amounts set forth on Exhibit A.

            (b) Execution of Counterparts. The Lenders shall have received
counterparts of this Amendment, duly executed by and delivered on behalf of each
of the Loan Obligors and each of the Lenders.

            (c) Fees and Expenses. The Lenders shall have received $15,000
representing certain amounts due and payable to Willkie Farr & Gallagher counsel
to the Lenders.


                                       3
<PAGE>
            (d) Deadline. The foregoing conditions in this Section 3.1 shall
have been satisfied on or before October 10, 2001.

                                  ARTICLE IV.

                         REPRESENTATIONS AND WARRANTIES

            SECTION 4.1. Representations and Warranties. In order to induce the
Lenders to enter into this Amendment, Each Loan Obligor, hereby represents and
warrants jointly and severally to each Lender, as of the date hereof and as of
the Amendment Effective Date, as follows:

            (a) Good Standing and Power. Each Loan Obligor is duly organized,
validly existing and in good standing under the laws of the jurisdiction of its
organization, has the requisite power and authority to own its property and
assets and to carry on its business as now conducted and as currently proposed
to be conducted..

            (b) Corporate Authority. Each Loan Obligor has full corporate power
and authority to execute, deliver and perform this Amendment. the Amended
Security Agreement and the Amended Credit Agreement and to incur the obligations
provided for herein and therein, all of which have been duly authorized by all
proper and necessary corporate action. No consent or approval of stockholders is
required as a condition to the validity or performance or the exercise by each
of the Lenders of any of its rights or remedies under the Amended Credit
Agreement or the Amended Security Agreement.

            (c) Authorizations. All authorizations, consents, approvals,
registrations, notices, exemptions and licenses with or from governmental
authorities and other persons, if any, which are necessary for the execution and
delivery of this Amendment, the performance by each of the Loan Obligor's of its
obligations hereunder and under the Amended Credit Agreement and the Amended
Security Agreement and the exercise by each of the Lenders of its rights and
remedies hereunder and thereunder, have been effected or obtained and are in
full force and effect.

            (d) Binding Agreements. This Amendment, the Amended Credit Agreement
and the Amended Security Agreement constitute the valid and legally binding
obligations of each Loan Obligor enforceable in accordance with their terms
subject to bankruptcy, insolvency, fraudulent transfer, reorganization,
moratorium and similar laws of general applicability relating to or affecting
creditors rights and to general equity principles.

            (e) No Conflicts. There is no statute, regulation, rule, order or
judgment, and no provision of any agreement or instrument binding on any Loan
Obligor or affecting its properties and no provision of the certificate of
incorporation or by-laws of any Loan Obligor, which would prohibit, conflict
with or in any way prevent the execution, delivery, or performance of the terms
of this Amendment, the Amended Credit Agreement or the Amended Security
Agreement or the incurrence of the obligations provided for herein and therein,
or result in or require the creation or imposition of any lien, security
interest or other encumbrance (other than in favor of the Lenders) on any of the
Loan Obligors' properties as a consequence of the execution, delivery and


                                       4
<PAGE>
performance of this Amendment, the Amended Credit Agreement or the Amended
Security Agreement or the transactions contemplated hereby and thereby.

            (f) No Default. As of the date hereof, but prior to giving effect to
this Amendment, there does not exist any Event of Default or event which, upon
the giving of notice or lapse of time or both, would constitute an Event of
Default.

                                   ARTICLE V.

                                  MISCELLANEOUS

            SECTION 5.1. Full Force and Effect; Limited Amendment. Except as
expressly modified hereby, all of the representations, warranties, terms,
covenants, conditions and other provisions of the Credit Agreement, the Security
Agreement and the Revolving Credit Notes shall remain unamended and unwaived and
shall continue to be, and shall remain, in full force and effect in accordance
with their respective terms. The amendments set forth herein shall be limited
precisely as provided for herein to the provisions expressly amended herein and
shall not be deemed to be a waiver to, consent to or modification of any other
term or provision of the Credit Agreement, the Security Agreement or any
Revolving Credit Note or of any transaction or further or future action on the
part of the which would require the consent of the Lenders under the Credit
Agreement.

            SECTION 5.2. Loan Document Pursuant to Credit Agreement. This
Amendment is executed pursuant to the Credit Agreement and shall be construed,
administered and applied in accordance with all of the terms and provisions of
the Credit Agreement (and, following the Amendment Effective Date, the Amended
Credit Agreement). Any breach of any representation or warranty or covenant or
agreement contained in this Amendment shall be deemed to be an Event of Default
for all purposes of the Amended Credit Agreement.

            SECTION 5.3. Subsidiary Acknowledgement. Each of the Subsidiaries
hereby expressly (i) ratifies and affirms its obligations under the Loan
Documents (as defined in the Credit Agreement) including guarantees, security
agreements and pledge agreements) executed and delivered by the Subsidiaries for
the benefit of the Lenders, (ii) acknowledges, renews and extends its continued
liability under all such Loan Documents and agrees such Loan Documents remain in
full force and effect, including with respect to the obligations of the Loan
Obligors as modified by the foregoing Amendment and (iii) acknowledges and
agrees that its obligations under the Loan Documents include the obligations
under this Amendment.

            SECTION 5.4. Fees and Expenses. The Borrower shall pay $15,000
representing amounts incurred by the Lenders in connection with the preparation,
negotiation, execution and delivery of this Amendment and the documents and
transactions contemplated hereby.

            SECTION 5.5. Headings. The various headings of this Amendment are
inserted for convenience only and shall not affect the meaning or interpretation
of this Amendment or any provisions hereof.


                                       5
<PAGE>
            SECTION 5.6. Execution in Counterparts. This Amendment may be
executed by the parties hereto in several counterparts, each of which shall be
deemed to be an original and all of which shall constitute together but one and
the same agreement.

            SECTION 5.7. Cross-References. References in this Amendment to any
Article or Section are, unless otherwise specified or otherwise required by the
context, to such Article or Section of this Amendment.

            SECTION 5.8. Successors and Assigns. This Amendment shall be binding
upon and inure to the benefit of the parties hereto and their respective
successors and assigns.

            SECTION 5.9. GOVERNING LAW. THIS WAIVER SHALL BE DEEMED TO BE A
CONTRACT MADE UNDER AND GOVERNED BY THE LAWS OF THE STATE OF NEW YORK WITHOUT
REGARD TO ITS CONFLICTS OF LAW DOCTRINE.


                                       6
<PAGE>
            IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be duly executed as of the date first above written.

                                        BORROWER:

                                        APPLIEDTHEORY CORPORATION

                                        By:  /s/ Danny E. Stroud
                                             -----------------------------------
                                             Name:  Danny E. Stroud
                                             Title: President


                                        SUBSIDIARIES:

                                        APPLIEDTHEORY GEORGIA CORPORATION

                                        By:  /s/ Danny E. Stroud
                                             -----------------------------------
                                             Name:  Danny E. Stroud
                                             Title: President


                                        APPLIEDTHEORY SEATTLE CORPORATION

                                        By:  /s/ Danny E. Stroud
                                             -----------------------------------
                                             Name:  Danny E. Stroud
                                             Title: President


                                        APPLIEDTHEORY CALIFORNIA CORPORATION

                                        By:  /s/ Danny E. Stroud
                                             -----------------------------------
                                             Name:  Danny E. Stroud
                                             Title: President


                                        APPLIEDTHEORY VIRGINIA CORPORATION

                                        By:  /s/ Danny E. Stroud
                                             -----------------------------------
                                             Name:  Danny E. Stroud
                                             Title: President


                                        APPLIEDTHEORY AUSTIN CORPORATION

                                        By:  /s/ Danny E. Stroud
                                             -----------------------------------
                                             Name:  Danny E. Stroud
                                             Title: President
<PAGE>
                                        APPLIEDTHEORY COLORADO CORPORATION

                                        By:  /s/ Danny E. Stroud
                                             -----------------------------------
                                             Name:  Danny E. Stroud
                                             Title: President
<PAGE>
                                        LENDERS:

                                        HALIFAX FUND, L.P.
                                        By: The Palladin Group, L.P.,
                                            as Attorney-in-Fact


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


                                        PALLADIN PARTNERS I, L.P.
                                        By: The Palladin Group, L.P.,
                                            as Attorney-in-Fact


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


                                        PALLADIN OVERSEAS FUND LTD.
                                        By: The Palladin Group, L.P.,
                                            as Attorney-in-Fact


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


                                        DeAM CONVERTIBLE ARBITRAGE FUND, LTD.
                                        By: The Palladin Group, L.P.,
                                            as Attorney-in-Fact


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


                                        LANCER SECURITIES (CAYMAN) LTD.
                                        By: The Palladin Group, L.P.,
                                            as Attorney-in-Fact


                                        By:  /s/ Maurice Hryshko
                                             -----------------------------------
                                             Name:  Maurice Hryshko
                                             Title: Counsel
<PAGE>
                                        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., as Attorney-in-Fact


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