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                                                                   EXHIBIT 10.34


                             TRANSITION AGREEMENT

This Agreement ("Agreement") is effective as of the Effective Time of the merger
pursuant to the Merger Agreement (as defined in Recital A below) (the "Effective
Date") among Global Crossing Ltd., a company organized under the laws of Bermuda
("Global Crossing Ltd"), Global Crossing North America, Inc., a New York
corporation and a direct subsidiary of Global Crossing Ltd ("Global Crossing
NA"), Global Crossing GlobalCenter Holding Co., a Delaware corporation and an
indirect subsidiary of Global Crossing NA ("GCG"), Exodus Communications, Inc.,
a Delaware corporation ("Exodus"), GlobalCenter Holding Co., a Delaware
corporation and a direct subsidiary of GCG to be merged with and into a direct
subsidiary of Exodus (the "Company"), and GlobalCenter, Inc., a Delaware
corporation and a direct wholly owned subsidiary of the Company
("GlobalCenter").  For the purposes of this Agreement, "Suppliers" shall mean
Global Crossing Ltd, Global Crossing NA and GCG, jointly and severally, and
"Recipients" shall mean the Company and GlobalCenter, jointly and severally.
Capitalized terms not otherwise defined in this Agreement shall have the
meanings set forth in the Merger Agreement.

                                   RECITALS

     A.   The parties have entered into an Agreement and Plan of Merger (the
          "Merger Agreement") and other related agreements dated September 28,
          2000.

     B.   Pursuant to the Merger Agreement, Exodus Merger Sub, a Delaware
          corporation and a direct subsidiary of Exodus ("Exodus Merger Sub")
          shall be merged with and into the Company, such that the separate
          corporate existence of Exodus Merger Sub shall cease and the Company
          shall continue as the surviving corporation.  The common stock of
          Company shall be converted into the common stock of Exodus.
          Accordingly, the Merger Agreement shall have the effect that, after
          the Closing, the Recipients shall cease to be direct and indirect
          subsidiaries of the Suppliers, and shall become the direct and
          indirect subsidiaries of Exodus.

     C.   The parties agree that Exodus and the Recipients shall require the
          Suppliers to continue to provide to the Recipients certain Services
          after the Closing that the Suppliers had been providing to Recipients
          before the Closing, in order to support the transition of the
          Recipients' business with minimal disruption.

                                   AGREEMENT

NOW, THEREFORE, in consideration of the conditions and covenants contained in
this Agreement, the parties agree as follows:

     1.   Provision of Services.  Suppliers shall provide to Recipients all
          services and resources that Suppliers had been providing to Recipients
          during the six (6) month period before the Effective Time other than
          (i) those services governed by the Network Services, Marketing and
          Cooperation Agreements with Global Crossing Ltd. and Asia Global
          Crossing Ltd. entered into simultaneously with the Merger Agreement
          (the "Network Agreements"), and (ii) for the avoidance of doubt, any
<PAGE>

          products provided by Suppliers to Recipients including those governed
          by the Network Agreements.  The services to be provided hereunder
          include, but are not limited to, those services and resources that may
          be specified in Statements of Work to be attached from time to time to
          this Agreement executed by the authorized representative of the
          Suppliers and of the Recipients (the "Services").

          Any further Statements of Work shall become effective when executed by
          an authorized representative of the Suppliers and of the Recipients.
          The Suppliers shall jointly authorize a single representative for this
          purpose, and the Recipients shall also jointly authorize a single
          representative for this purpose.

          Recipients shall pay Suppliers for the Services at a price equal to a
          bona fide third party quote for the same bundle of services being
          provided.  The terms and conditions of this Agreement shall be deemed
          incorporated into each Statement of Work, unless otherwise expressly
          indicated in such Statement of Work.

     2.   Statements of Work.  Each Statement of Work shall be substantially in
          the form of Appendix A hereto and shall contain the following
          information, as applicable, plus any other applicable terms and
          conditions:

          (a)  Identification.  Each individual Statement of Work shall be
               --------------
               identified by a title, the effective date of the Statement of
               Work, and reference to this Agreement;

          (b)  Required Contents.  Each Statement of Work may contain (or
               -----------------
               incorporate as attachments or by reference):

               (i)    Brief description of the scope of the Services to be
                      performed under the Statement of Work;

               (ii)   Designation of a Project Manager or contact person for
                      each party and their addresses, telephone numbers and
                      facsimile numbers;

               (iii)  Detailed description of the Services Suppliers are to
                      perform, the number of persons required to perform the
                      Services, and the time schedule for provision of such
                      Services;

               (iv)   Anticipated duration of the Services;

               (v)    Description of Recipients' responsibilities associated
                      with the Services, if any;

               (vi)   The notice period required for Recipients to terminate the
                      Services; and

               (vii)  A description of any amount to be paid to Suppliers by
                      Recipients for the Services, including the unit and
                      aggregate amounts, as applicable, the method of
                      calculation, the schedule of payments, and address to
                      which such payments are to be made; and
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          (c)  Project Managers.  Unless otherwise specified in a Statement of
               ----------------
               Work, the Recipients and Suppliers shall each name one "Project
               Manager" who shall be responsible for managing the performance of
               those parties under the Statement of Work and for all necessary
               coordination with the other party with respect to the Services
               identified in such Statement of Work.  Each party shall advise
               the other in writing of any change to its Project Manager.

     3.   Effect of Providing Services.  Recipients shall remain responsible
          for, and shall have the final authority to make, all decisions
          regarding the business and other operations of the Recipients.  The
          parties shall consult with each other regarding any significant
          changes to the Services required to accommodate any changes made by
          Recipients to their business or other operations.

     4.   Reciprocal Representations and Warranties.  Each party represents and
          warrants that:

          (a)  it has full corporate power and authority to enter into this
               Agreement and perform its obligations under this Agreement; and

          (b)  the execution and delivery of this Agreement shall not conflict
               with or result in the breach of any agreement or other legal
               obligation to which that party is subject.

     5.   Representations and Warranties.  Suppliers jointly and severally
          represent and warrant to Recipients and to Exodus that Suppliers shall
          provide the Services to Recipients in a manner substantially
          consistent with the provision of such services during the 6 months
          prior to the Effective Time.

     6.   Limitation on Liability.

          (a)  Except for the representation contained in Section 5 all Services
               will be provided without representation or warranty of any kind
               and Suppliers shall not have any liability to Recipients arising
               out of or relating to the provision of the Services except for
               any liability arising from a breach of Section 5 or from the
               gross negligence or willful misconduct of Suppliers.  THE LIMITED
               WARRANTIES SET FORTH ABOVE ARE EXCLUSIVE AND ARE IN LIEU OF ALL
               OTHER WARRANTIES AND CONDITIONS, EXPRESS, IMPLIED, STATUTORY OR
               OTHERWISE WITH RESPECT TO THE SERVICES OR PRODUCTS PROVIDED UNDER
               THIS AGREEMENT, THE PERFORMANCE OF MATERIALS OR PROCESSES
               DEVELOPED OR PROVIDED UNDER THIS AGREEMENT, OR AS TO THE RESULTS
               WHICH MAY BE OBTAINED THEREFROM, AND ALL IMPLIED WARRANTIES AND
               CONDITIONS OF MERCHANTABLITY, FITNESS FOR A PARTICULAR PURPOSE,
               TITLE AND NONINFRINGEMENT.

          (b)  TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, IN NO EVENT
               SHALL ANY PARTY, ITS SUBSIDIARIES,
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               AFFILIATES OR THEIR RESPECTIVE SUPPLIERS BE LIABLE FOR ANY
               INCIDENTAL, CONSEQUENTIAL, INDIRECT, SPECIAL, OR PUNITIVE DAMAGES
               (INCLUDING, BUT NOT LIMITED TO, LOST PROFITS, BUSINESS
               INTERRUPTION, LOSS OF BUSINESS INFORMATION OR OTHER PECUNIARY
               LOST) REGARDLESS OF WHETHER SUCH LIAIBILITY IS BASED ON BREACH OF
               CONTRACT, TORT (INCLUDING NEGLIGENCE), STRICT LIABILITY, BREACH
               OF WARRANTIES, FAILURE OF ESSENTIAL PURPOSE OR OTHERWISE AND EVEN
               IF ADVISED OF THE POSSIBLITY OF SUCH DAMAGES.

     7.   Confidentiality.  During and after the term of this Agreement, a party
          ("Disclosee") that receives or gains access to the Confidential
          Information of the other party ("Discloser"):

          (a)  may use the Discloser's Confidential Information only in
               connection with performing its obligations under this Agreement;

          (b)  must not disclose the Discloser's Confidential Information to any
               third party other than its employees, affiliates, vendor
               contractors and advisers that: (i) need to know the Confidential
               Information in connection with the Services, and (ii) are subject
               to an obligation to maintain the confidentiality of the
               Confidential Information at least as restrictive as this
               Section 7;

          (c)  must implement reasonable security procedures and standards of
               care to prevent unauthorized disclosure or use of Discloser's
               Confidential Information, at least to the same standard that it
               uses with its own information of similar sensitivity and
               importance; and

          (d)  must destroy or return to the Discloser the Confidential
               Information promptly on the termination of this Agreement or as
               otherwise directed by the Discloser.

          "Confidential Information" means any business, financial, personnel or
          technical information relating to the business or other activities of
          the Discloser that the Disclosee obtains in connection with this
          Agreement, but excludes any information that:

          (a)  is in the public domain or is generally known or available
               otherwise than through a breach of confidence by or through the
               Disclosee;

          (b)  is obtained or developed by the Disclosee, independently of the
               Discloser's Confidential Information, without violating any
               confidentiality restriction and without any restriction on the
               Disclosee's further use or disclosure;

          (c)  is permitted for release or disclosure to any third party by the
               written prior consent of the Discloser; or

          (d)  the Disclosee is required by an applicable law to disclose, to
               the extent of that legal disclosure obligation, provided that the
               Disclosee gives the Discloser prompt notice of that requirement.
<PAGE>

     8.   Termination.  Unless otherwise agreed by the parties in writing, this
          Agreement shall automatically terminate on the earliest of:

          (a)  any termination of the Merger Agreement pursuant to Section 7.1
               of the Merger Agreement; or

          (b)  the date that is one (1) year after the Effective Time, provided
               however each Statement of Work shall continue after that
               termination date to the extent required to complete all Services
               specified in that Statement of Work; or

          (c)  a date nominated by the Recipients in any termination notice,
               such termination to be for any reason or for no reason at all,
               provided that the termination date is at least seven (7) days
               after the date of the termination notice.

     9.   General.

          (a)  Relationship of Parties.  The relationship between the parties is
               -----------------------
               that of independent contractors.  This Agreement shall not be
               construed as creating an employee/employer, agency, partnership
               or joint venture relationship between the parties.  Suppliers are
               not representatives or agents of Recipients for any purpose and
               have no authority to enter into agreements or other legal
               relations or obligations that are enforceable against Recipients.
               Except as expressly required by this Agreement, Suppliers shall
               not take any actions on Recipients' behalf.  Suppliers shall not
               take any action or make any communication indicating that
               Suppliers are representatives or agents of Recipients.

          (b)  Governing Law and Choice of Venue.  This Agreement shall be
               ---------------------------------
               governed by the internal laws of the State of California without
               reference to conflict of laws principals.  Each party irrevocably
               consents to the jurisdiction of the state and federal courts
               located in California in connection with any action or proceeding
               arising from or relating to this Agreement or its subject matter.

          (c)  Amendment and Waivers.  Any term or provision of this Agreement
               ---------------------
               may be amended, and the observance of any term of this Agreement
               may be waived (either generally or for any particular instance
               and either retroactively or prospectively) only by a writing
               signed by the party to be bound thereby.

          (d)  Non-waiver.  The failure of any party to enforce at any time any
               ----------
               of the provisions of this Agreement shall not be construed to be
               a waiver of the right of such party thereafter to enforce any
               such provision.

          (e)  Severability.  If for any reason a court of competent
               ------------
               jurisdiction finds any provision or portion of this Agreement to
               be unenforceable, that provision of the Agreement will be
               enforced to the maximum extent permissible so
<PAGE>

               as to effect the intent of the parties, and the remainder of this
               Agreement will continue in full force and effect.

          (e)  Notices.  Notices and other communications under this Agreement
               -------
               shall be given, and shall be deemed delivered, in the manner
               specified for delivery of notices in the Merger Agreement.

          (f)  Entire Agreement.  This Agreement supersedes all proposals, oral
               ----------------
               or written, and all negotiations, conversations or discussions
               between or among parties relating to the subject matter of this
               Agreement and all past dealings or industry customs.

          (g)  Assignment:  Binding upon Successors and Assigns.  A party may
               ------------------------------------------------
               not assign any of its rights or obligations under this Agreement
               without the prior written consent of the other parties.  This
               Agreement shall be binding upon and inure to the benefit of the
               each party and its respective successors and permitted assigns.

          (h)  Counterparts.  This Agreement may be executed in any number of
               ------------
               counterparts, each of which shall be an original as regards to
               any party whose signature appears thereon and all of which
               together shall constitute one and the same instrument.  This
               Agreement shall become binding when one or more counterparts of
               it, individually or taken together, bear the signature of each of
               the parties.

          (i)  Construction.  This Agreement has been negotiated by the parties
               ------------
               and its language shall not be construed for or against either
               party.  Headings and titles in this Agreement are for reference
               purposes only and do not constitute part of this Agreement.

          (j)  Expenses.  Each party shall bear its respective expenses and
               --------
               legal fees incurred with respect to this Agreement, and the
               transactions contemplated hereby.

     10.  Force Majeure.  If Suppliers are prevented from providing, either
          totally or in part, any Services by reason of fire, flood, storm,
          strike, lockout or other labor trouble, riot, war, rebellion, accident
          or other acts of God, then upon written notice to the Recipients, the
          requirements of this Agreement to provide such Services or the
          affected provisions hereof to the extent affected, shall be suspended
          during the period of such disability, provided that Suppliers give
          Recipients prompt notice of the cause of the suspension, the reasons
          for it, its expected duration and any work around plans for the
          Services suspended.


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<PAGE>

IN WITNESS WHEREOF, the parties hereto have executed this Transition Agreement
effective as of the date first above written.

"Suppliers"                                "Recipients"

Global Crossing Ltd.                       GlobalCenter Holding Co.

Signature /s/ James C. Gorton              Signature  /s/ Leo J. Hindery, Jr.
          --------------------------                 ---------------------------
Name      James C. Gorton                  Name       Leo J. Hindery, Jr.
          --------------------------            --------------------------------
Title     Executive Vice President         Title      Chief Executive Officer
          and General Counsel                    -------------------------------
          --------------------------


Global Crossing North                      GlobalCenter Inc.

America, Inc.

Signature /s/ Joseph P. Clayton            Signature  /s/ Leo J. Hindery, Jr.
          --------------------------                 ---------------------------
Name      Joseph P. Clayton                Name       Leo J. Hindery, Jr.
          --------------------------            --------------------------------
Title     Chief Executive Officer          Title      Chief Executive Officer
          --------------------------             -------------------------------


Global Crossing GlobalCenter               Exodus Communications, Inc.
Holdings, Inc.

Signature /s/ Leo J. Hindery, Jr.          Signature  /s/ Ellen M. Hancock
          --------------------------                 ---------------------------
Name      Leo J. Hindery, Jr.              Name       Ellen M. Hancock
          --------------------------            --------------------------------
Title     Chief Executive Officer          Title      Chief Executive Officer
          --------------------------                  and Chairman
                                                 -------------------------------
<PAGE>

                                  Appendix A

                               STATEMENT OF WORK

                                      for

                            ADMINISTRATION SERVICES

                         Effective on __________, 2000

         Under the Transition Agreement dated ___________, 2000 among

Global Crossing Ltd, a Bermuda Corporation ("Global Crossing Ltd"), Global
Crossing North America, Inc., a New York corporation and a direct subsidiary of
Global Crossing Ltd ("Global Crossing NA"), Global Crossing GlobalCenter
Holdings, Inc., a Delaware corporation and a direct subsidiary of Global
Crossing NA ("GCG"), EXODUS, a Delaware corporation ("Exodus"), GlobalCenter
Holding Co., a Delaware corporation and a direct subsidiary of GCG to be merged
with and into a direct subsidiary of Exodus (the "Company"), and GlobalCenter
Inc., a Delaware corporation and a direct subsidiary of the Company
("GlobalCenter").  "Suppliers" shall mean Global Crossing Ltd, Global Crossing
NA and GCG, jointly and severally, and "Recipients" shall mean the Company and
GlobalCenter, jointly and severally.

The terms of the Transition Agreement between the parties are incorporated in
this Statement of Work by this reference.

1.   The following is a brief description of the scope of the Services
(including resources) to be performed by Suppliers under this Statement of Work:

ADMINISTRATION

  Payroll - Suppliers provide all payroll and related functions.

  Benefits and Human Resources - [Insert who performs and where]

  Travel Services - Recipients utilize the travel professionals under contract
  with [Insert whom].


2.   Project Managers shall be as follows:

For Suppliers:                      For Recipients:
--------------                      ---------------

Name:                               Name:

Address:                            Address:

Telephone:                          Telephone:

Fax:                                Fax:
<PAGE>

3.   Detailed description of Services (including resources) Suppliers is to
provide and the time schedule for provision of the Services:


4.   The number and names of the persons required to provide the Services:


5.   The anticipated duration of the Services:


6.   Notice period required for Recipients to terminate the Services:


7.   Description of Recipient's responsibilities associated with the Services,
if any, Suppliers are to perform:


8.   Description of the amount payable by Recipients to Suppliers for the
Services, including the unit and aggregate amounts, if applicable, the method of
calculation, schedule of payments, and address to which such payments are to be
made:


9.   The names of individual contractors and consultants, if any, Suppliers will
use to perform any part of the Services:


     Recipients hereby consent to Suppliers' use of such listed independent
contractors and consultants.


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<PAGE>

     Any further Statement of Work shall be effective as of the date first
indicated above once it has been executed by a duly authorized representative of
each of Recipients and Suppliers.


"Suppliers"                      "Recipients"


Signature                          Signature
          ----------------                    --------------------

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

Title                              Title
          ----------------                    --------------------

Date                               Date
          ----------------                    --------------------