<PAGE>
 
                                                                   EXHIBTI 10.21
 
                        MANAGEMENT CONSULTING AGREEMENT


                                    BETWEEN


                               XTRA CORPORATION


                                      AND


                          APOLLO MANAGEMENT IV, L.P.



                       Dated as of _______________, 1998
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     MANAGEMENT CONSULTING AGREEMENT, dated as of _____________________,
1998 (this "Agreement"), between XTRA CORPORATION, a Delaware corporation (the
"Company"), and APOLLO MANAGEMENT IV, L.P., a Delaware limited partnership
(Apollo").
 
     WHEREAS, the Company desires to avail itself of Apollo's expertise and
consequently has requested Apollo to make such expertise available from time to
time in rendering certain management consulting and advisory services related to
the business and affairs of the Company and its respective subsidiaries and
affiliates and the review and analysis of certain financial and other
transactions.  Apollo and the Company agree that it is in their respective best
interests to enter into this Agreement whereby, for the consideration specified
herein, Apollo has provided and shall provide such services as independent
consultant to the Company.

     NOW, THEREFORE, in consideration of the mutual covenants hereinafter set
forth, the Company and Apollo agree as follows:

     SECTION 1.     RETENTION OF APOLLO.
                    ------------------- 

     The Company hereby retains Apollo, and Apollo accepts such retention, upon
the terms and conditions set forth in this Agreement.

     SECTION 2.     TERM.
                    ---- 

     This Agreement shall commence on the date hereof and, unless earlier
terminated pursuant to the final sentence of this Section 2, shall terminate on

September __, 2008 (the "Initial Term").  Notwithstanding the foregoing, the
                         ------------                                       
Company may terminate this Agreement concurrently with any sale of the Company
as a going concern to an unaffiliated third party (whether by merger, sale of
substantially all of its assets or otherwise), if after such transaction none
of Apollo, any affiliate of Apollo, any limited or general partner of Apollo or
any of their respective Affiliates owns, directly or indirectly, individually or
in the aggregate, more than five percent of the equity interest in the Company
or the Company's purchaser.

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     SECTION 3.     MANAGEMENT CONSULTING SERVICES.
                    ------------------------------ 

          (a)  Apollo shall advise and assist the Company concerning such
management matters that relate to proposed financial transactions, acquisitions
and other senior management matters related to the business, administration and
policies of the Company and its subsidiaries and affiliates, in each case as the
Company shall reasonably and specifically request by way of written notice to
Apollo, which notice shall specify the services required of Apollo and shall
include all background material necessary for Apollo to complete such services.
Apollo shall devote such time to any such written request as Apollo shall deem,
in its discretion, necessary. Such consulting services, in Apollo's discretion,
shall be rendered in person or by telephone or other communication.  Apollo
agrees to perform the services requested by the Company in a professional manner
as it shall reasonably determine in order for the Company to analyze the matter
for which Apollo's services were requested.

          (b)  The Company acknowledges and agrees that Apollo (i) has
structured the recapitalization and the other transactions contemplated by the
Agreement and Plan of Merger and Recapitalization, dated as of June 18, 1998, as
amended (the "Recapitalization Merger Agreement"), between Wheels MergerCo LLC
              ---------------------------------                               
and the Company, (ii) has arranged for financing in connection with the
recapitalization, and (iii) has provided other services in connection with the
transactions contemplated by the Recapitalization Merger Agreement.  Apollo
agrees to continue to provide services to the Company in connection with the
consummation of the transactions contemplated by the Merger Agreement.

          (c)  Apollo shall perform all services to be provided hereunder as an
independent contractor to the Company and not as an employee, agent or
a representative of the Company. Apollo shall have no authority to act
for or to bind the Company, without its prior written consent.

          (d)  This Agreement shall in no way prohibit Apollo or any of its
partners or Affiliates or any director, officer, partner or employee of Apollo
or any of its partners or Affiliates from engaging in other activities, whether
or not competitive with any business of the Company or any of its respective
subsidiaries or Affiliates.

     SECTION 4.     COMPENSATION.
                    ------------

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          (a)  As consideration for Apollo's agreement to render the services
set forth in Section 3(a) of this Agreement and as compensation for any such
services rendered by Apollo, the Company agrees to pay to Apollo an annual fee
of $1,000,000 payable in equal quarterly installments of $250,000 each on the
first day of each fiscal quarter (or, if such date is not a business day, on the
next business day thereafter).

          (b)  As consideration for services rendered and Apollo's agreement to
render services as set forth in Section 3(b), the Company (on behalf of itself
and the Surviving Corporation) agrees to pay to Apollo a fee of $12,500,000
which shall be earned upon consummation of the transactions contemplated by the
Recapitalization Merger Agreement.

          (c)  Upon presentation by Apollo to the Company of such documentation
as may be reasonably requested by the Company, the Company shall reimburse
Apollo for all out-of-pocket expenses, including, without limitation, legal fees
and expenses, and other disbursements incurred by Apollo, its Affiliates or any
if its Affiliates' directors, officers, employees or agents in the performance
of Apollo's obligations hereunder, whether incurred on or prior to the date
hereof, including, without limitation, out-of-pocket expenses incurred in
connection with the transactions contemplated by the Recapitalization Merger
Agreement.

          (d)  Nothing in this Agreement shall have the effect of prohibiting
Apollo or any of its Affiliates from receiving from the Company or any of its
subsidiaries of Affiliates any other fees, including any fee payable pursuant to
Section 6.

     SECTION 5.     INDEMNIFICATION.
                    --------------- 

     The Company agrees that it shall indemnify and hold harmless Apollo, its
Affiliates and its Affiliates' directors, officers, employees and agents
(collectively, the "Indemnified Persons") on demand from and against any and all
                    -------------------                                         
liabilities, costs, expenses and disbursements (collectively, "Claims") of any
                                                               ------         
kind with respect to or arising from this Agreement or the performance by any
Indemnified Person of any services in connection herewith.  Notwithstanding the
foregoing provision, the Company shall not be liable for any Claim under this
Section 5 arising from the willful misconduct of any Indemnified Person.

     SECTION 6.     OTHER SERVICES.
                    -------------- 

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     If the Company shall determine that it is advisable for the Company to hire
a financial advisor, consultant, investment banker or any similar agent in
connection with any merger, acquisition, disposition, issuance of securities,
financing or any similar transaction, it shall notify Apollo of such
determination in writing.  Promptly thereafter, upon the request of Apollo, the
parties shall negotiate in good faith to agree upon appropriate services,
compensation and indemnification for the Company to hire Apollo or its
Affiliates for such services.  The Company may not hire any person, other than
Apollo or its Affiliates, for any services, unless (a) the parties are unable to
agree after 30 days following receipt by Apollo of such written notice, (b) such
other person has a reputation that is at least equal to the reputation of Apollo
in respect of such services, (c) ten business days shall have elapsed after the
Company provides a written notice to Apollo of its intention to hire such other
person, which notice shall identify such other person and shall describe in
reasonable detail the nature of the services to be provided, the compensation to
be paid and the indemnification to be provided and (d) the compensation to be
paid is not more than Apollo was willing to accept in the negotiations described
above, and (e) the idemnification to be provided is not more favorable to the
Company than the indemnification that Apollo was willing to accept in the
negotiations described above.

     SECTION 7.     NOTICES.
                    ------- 

     All notices, requests, consents and other communications hereunder shall be
in writing and shall be deemed sufficient if personally delivered, sent by
nationally-recognized overnight courier, by telecopy, or by registered or
certified mail, return receipt requested and postage prepaid, addressed as
follows:

          if to Apollo, to:

               Apollo Management IV, L.P.
               1301 Avenue of the Americas
               38/th/ Floor
               New York, New York  10019
               Attention:  Mr. Andrew Africk
               Telecopier:  (212) 261-4071

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          if to the Company:

               XTRA Corporation
               1801 Park 270 Drive,
               Suite 400
               St. Louis, MO 63146
               Telecopier: (314) 579-9300

or to such other address as the party to whom notice is to be given may have
furnished to each other party in writing in accordance herewith.  Any such
notice or communication shall be deemed to have been received (a) in the case of
personal delivery, on the date of such delivery, (b) in the case of nationally-
recognized overnight courier, on the next business day after the date when sent,
(c) in the case of telecopy transmission, when received, and (d) in the case of
mailing, on the third business day following that on which the piece of mail
containing such communication is posted.

     SECTION 8.     BENEFITS OF AGREEMENT.
                    --------------------- 

     This Agreement shall bind and inure to the benefit of Apollo, the Company,
the Indemnified Persons and any successors to or assigns of Apollo and the
Company; provided, however, that this Agreement may not be assigned by either
         --------  -------
party hereto without the prior written consent of the other party, which consent
will not be unreasonably withheld in the case of any assignment by Apollo. The
foregoing notwithstanding, Apollo may assign a portion of its fees hereunder to
any person assisting Apollo in the performance of its duties hereunder.

     SECTION 9.     GOVERNING LAW.
                    ------------- 

     This Agreement shall be governed by and construed and enforced in
accordance with the laws of the State of New York (without giving effect to
principles of conflicts of laws).

     SECTION 10.    HEADINGS.
                    -------- 

     Section headings are used for convenience only and shall in no way affect
the construction of this Agreement.

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     SECTION 11.    ENTIRE AGREEMENT; AMENDMENTS.
                    ---------------------------- 

     This Agreement contains the entire understanding of the parties with
respect to its subject matter, and neither it nor any part of it may in any way
be altered, amended, extended, waived, discharged or terminated except by a
written agreement signed by each of the parties hereto.

     SECTION 12.    COUNTERPARTS.
                    ------------ 

     This Agreement may be executed in counterparts, and each such counterpart
shall be deemed to be an original instrument, but all such counterparts together
shall constitute but one agreement.

     SECTION 13.    WAIVERS.
                    ------- 

     Any party to this Agreement may, by written notice to the other party,
waive any provision of this Agreement.  The waiver by any party of a breach of
any provision of this Agreement shall not operate or be construed as a waiver of
any subsequent breach.

     SECTION 14.    AFFILIATES.
                    ---------- 

     For purposes of this Agreement, the term "Affiliate," with respect to
Apollo, shall include, without limitation, Apollo Investment Fund IV, L.P.,
Apollo Overseas Partners IV, L.P., (collectively, the "Funds"), Apollo Advisors
IV, L.P., the general partner of Apollo, the general partner of each of the
Funds and each person controlling, controlled by or under common control with
any of the foregoing persons.

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          IN WITNESS WHEREOF, the parties have duly executed this Management
Consulting Agreement as of the date first above written.

                              XTRA CORPORATION


                              By:___________________________
                                  Name:
                                  Title:


                              APOLLO MANAGEMENT IV, L.P.


                              By:___________________________
                                  Name:
                                  Title:

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