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                                                                   EXHIBIT 10.31
                                 TAG-ALONG AGREEMENT



     THIS TAG-ALONG AGREEMENT (the "Agreement") dated as of November 17, 1997 is
among Prime Financing, L.P., Prime Group Limited Partnership, Prime Group II,
L.P., Prime Group III, L.P., Prime Group IV., L.P., Prime Group V, L.P., The
Prime Group, Inc., PG/Primestone, L.L.C., a Delaware limited liability company
(together with their respective controlled Affiliates and their successors in
interest pursuant to SECTION 4 hereof, the "Other Holders"), and Security
Capital Preferred Growth Incorporated, a Maryland corporation (together with its
successors in interest pursuant to SECTION 4 hereof, "SCPG").

                               PRELIMINARY STATEMENT

     WHEREAS the Other Holders own Common Units, which interests, subject to
certain conditions, are exchangeable for Common Shares.

     WHEREAS SCPG owns the Preferred Shares, which shares, subject to certain
conditions, are convertible into Common Shares.
     
     WHEREAS the Other Holders and SCPG desire to enter into this Agreement to
set forth certain agreements with respect to certain transfers by the Other
Holders of their Common Shares; and

     WHEREAS the execution and delivery of this Agreement by the parties hereto
is a condition to the closing of the Series A Preferred Securities Purchase
Agreement, dated as of November 11, 1997, by and among Prime Group Realty Trust,
Prime Group Realty, L.P. and SCPG.
     
     NOW THEREFORE, in consideration of the foregoing and other good and
valuable consideration, the receipt and sufficiency of which is hereby
acknowledged, the parties agree as follows:

     1.   DEFINITIONS.  As used in this Agreement, the following term shall have
the following meanings:

     "AFFILIATE" means, with respect to any Person, any other Person directly or
indirectly controlling, controlled by or under direct or indirect common control
with the first Person and shall include any Person who is an officer, director
or beneficial holder of at least 10% of the then outstanding capital stock (or
other shares of beneficial interest or partnership interest) of the first Person
entitled ordinarily to vote for the first Person's directors (or, for persons
that are not corporations, for those Persons exercising functions similar to
directors of a corporation) and immediate family members of any such officer,
director or holder.  

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     "COMMON SHARES" means the common shares of beneficial interest, $.01 par
value per share, of Prime Group Realty Trust and Common Share Equivalents.

     "COMMON SHARE EQUIVALENTS" means any security that is convertible into or
exchangeable for Common Shares or upon the exercise of which Prime Group Realty
Trust is required to issue Common Shares, whether or not such securities are
then convertible, exchangeable or exercisable.

     "COMMON UNITS" means the common units of limited partner interest of Prime
Group Realty, L.P.

     "EXTRAORDINARY TRANSACTION" means (a) any merger, consolidation,
recapitalization, other business combination or other similar action for which
approval of the holders of Common Shares is required and has been obtained, or
(b) any other Transfer (whether, pursuant to an exchange or tender offer or
otherwise) involving the sale or disposition of 80% or more of the then
outstanding Common Shares.    

     "PERSON" means any corporation, limited liability company, partnership,
association, organization, trust, individual, government or any agency or
political subdivision thereof, or other entity.

     "PREFERRED SHARES" means the shares of Series A cumulative convertible
preferred shares of beneficial interest, $.01 par value per share of Prime Group
Realty Trust.

     "SALE" means any Transfer by the Other Holders or by Primestone Investment
Partners, L.P. of Common Shares, directly or indirectly, to one or more Persons
who are not Affiliates controlled by the Other Holders if, after giving effect
to such Transfer and all prior Transfers of Common Shares during the preceding
12 months, the Other Holders and Primestone Investment Partners, L.P. will have
Transferred more than 15% of the number of Common shares beneficially owned by
the Other Holders and Primestone Investment Partners, L.P., in the aggregate, at
the beginning of such 12-month period (as adjusted for stock splits or stock
dividends, or in connection with a combination of shares, recapitalization,
merger, consolidation or other reorganization); provided, however, that the term
"Sale" shall not apply to Transfers by Primestone Investment Partners, L.P., the
proceeds of which are used either (a) to repay margin loan indebtedness of
Primestone Investment Partners, L.P. or (b) to fund distributions to affiliates
of The Blackstone Group.

     "SALE NOTICE" shall have the meaning ascribed to such items in SECTION 2(a)
of this Agreement.

     "SECURITIES ACT" means the Securities Act of 1933, as amended from time to
time.

     "TERMS NOTICE" shall have the meaning ascribed to such term in SECTION 2(b)
of this Agreement.

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     "TAG-ALONG RIGHTS" shall have the meaning ascribed to such term in SECTION
2 of this Agreement.

     "TRANSFER" means any direct or indirect sale, transfer, distribution,
assignment, bequest, pledge, hypothecation, encumbrance, grant of a security
interest in, or grant, issuance, sale or conveyance of an option, warrant or
right to acquire, or other disposition of, one or more Common Shares; provided,
however, that a Transfer shall not include (i) sales or dispositions made
pursuant to a broadly distributed, underwritten public offering pursuant to an
effective registration statement under the Securities Act, (ii) any pledge
(including any foreclosure or seizure resulting from such pledge) to a bona fide
financial institution or other business organization with a net worth in excess
of $25 million for the purpose of securing bona fide indebtedness (including any
guarantee or other obligation related thereto) of the Other Holders or (iii)
sales or dispositions pursuant to an Extraordinary Transaction.

     "TRANSFEREE" means the recipient, directly or indirectly, of one or more
Common Shares or any interest therein pursuant to a Transfer.

     2.   SALE OF COMMON SHARES.  The Other Holders agree, that in the event
that the Other Holders wish to engage in a Sale, to offer to SCPG the right to
participate in such sale in the manner and on the terms set forth in this
SECTION 2 (the rights of SCPG to participate in a Sale of Common Shares
hereunder are referred to herein as the "TAG-ALONG RIGHTS").

          (a)  OFFER.  At least three business days prior to any Sale, the Other
Holders shall deliver a written notice (the "SALE NOTICE") to SCPG which shall
include:

          (i)  A description of the proposed Sale, specifying in reasonable
detail the proposed terms and conditions of the proposed Sale, including the
number of Common shares proposed to be transferred as a result of such Sale, the
purchase price (or liquidation value) of such Shares, the name and address of
the proposed transferee(s), and the closing date of the proposed Sale.

          (ii) An offer by the Other Holders to include in the proposed Sale to
the proposed transferee, at the option of SCPG, on the same terms and conditions
as the proposed Sale, up to one Common Share for each two Common Shares to be
sold by the Other Holders in the proposed Sale.

          (b)  NOTICE OF PROPOSED SALE.  The Other Holders shall notify SCPG in
writing (the "TERMS NOTICE") of  the terms of the Sale as soon as practicable
after such terms are determined, but in any event at least one business day
prior to the Sale.

          (c)  TIME AND MANNER OF EXERCISE.  If SCPG desires to accept the offer
contained in the Sale Notice, it shall notify the Other Holders in writing
before 5:00 p.m. Chicago time on the business day following the date of receipt
of the Terms Notice, which notice shall specify the number of Common Shares for
which such offer has been accepted.  If SCPG has not so accepted such offer 

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in writing it shall be deemed to have waived all of its Tag-Along Rights with
respect to the proposed Sale, and the Other Holders shall be free, for a period
of 90 days from and after the date of receipt by SCPG of the Terms Notice, to
transfer the Common Shares specified in the Sale Notice but only on terms no
more favorable to the Other Holders than the terms described in the Sale Notice
and the Terms Notice, and any sale in violation of this provision shall be
invalid.

          (d)  OTHER AGREEMENTS.

          (i)    The Other Holders shall use their best efforts to obtain the
agreement of the prospective transferee(s) to the participation of SCPG in any
contemplated Sale, and the Other Holders shall not transfer any of their Common
Shares to the prospective transferee(s) if the prospective transferee(s)
declines to allow the participation of SCPG as contemplated by this Section 2,
and any sale in violation of this provision shall be invalid.  If SCPG elects to
exercise its Tag-Along Rights hereunder, SCPG shall take such actions and
execute such documents and instruments as may be requested by the Other Holders
and as shall be reasonably necessary in order to consummate the proposed Sale on
the same terms as the Other Holders.  Each of the Other Holders and SCPG shall
bear their or its own costs and expenses incurred in connection with any
proposed Sale.

          (ii)   Prime Group Realty Trust agrees that, if requested by SCPG in
writing, it will accelerate, pursuant to Section 3 of the Declaration creating
the Preferred Shares, the date on which the Preferred Shares are convertible so
as to permit SCPG to sell such number of Common Shares that it has elected to
sell pursuant to SECTION 2 of this Agreement.

          (iii)  PG/Primestone, L.L.C., as managing general partner of
Primestone Investment Partners, L.P., shall not vote for or consent to (and none
of the Other Holders shall vote or cause any of their Affiliates to vote for or
consent to) any sale of Common Shares by Primestone Investment Partners, L.P.
(except with respect to Transfers described in the Proviso to the definition of
"Sale" in Section 1 hereof) unless in connection with such Transfer, SCPG is
granted Tag-Along Rights in accordance with Section 2 hereof.

          (e)    ABANDONMENT OF SALE.  The Other Holders shall have the right,
in their sole discretion, at all times prior to consummation of the proposed
Sale to abandon, rescind, annul, withdraw or otherwise terminate such Sale, and
the Other Holders shall not have any liability or  obligation to SCPG with
respect thereto by virtue of such abandonment, rescission, annulment, withdrawal
or termination.

          3.     FORM OF AGREEMENT SATISFACTORY TO SCPG.  Any agreement which
SCPG may be requested or required to execute in connection with SECTION 2
hereof, must be in form and substance reasonably satisfactory to SCPG.  No
provision in this Agreement, including, without limitation, SECTION 2 hereof,
shall require SCPG to make any representation (other than as to title, due
authorization and enforceability relating solely to SCPG) or provide any
indemnification in any such agreement (other than indemnification for breaches
of the representations set forth in the preceding clause) and no right or
obligation of SCPG shall be conditioned upon the making of such 

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representation or the provision of such indemnification.

          4.     MISCELLANEOUS.

          (a)    NOTICES.  Notices and other communications provided for in
this Agreement shall be in writing and shall be either delivered by reputable
courier service (charges prepaid), sent by confirmed facsimile transmission or
sent by certified mail (postage prepaid and return receipt requested) addressed
to the party or parties sought to be charged with notice of the same at the
respective addresses set forth below, subject to written notice of change of
address given by any party to the other parties:

     IF TO THE OTHER
      HOLDERS:        The Prime Group, Inc.
                      77 West Wacker, Suite 3900
                      Chicago, Illinois  60601
                      Attention:  Michael W. Reschke
                                  Robert J. Rudnik
                      Fax:  (312) 917-1511

     with a copy to:  Wayne D. Boberg
                      Winston & Strawn
                      35 West Wacker Drive
                      Chicago, Illinois  60601
                      Fax:  (312) 558-5700

     IF TO SCPG:      Security Capital Preferred Growth Incorporated
                      11 South LaSalle Street
                      Chicago, Illinois  60603
                      Attention:  Daniel F. Miranda
                                  David E. Rosenbaum
                                  Joshua D. Goldman
                      Fax:  (312) 345-5888

     with a copy to:  Mayer, Brown & Platt
                      190 South LaSalle Street
                      Chicago, Illinois  60603
                      Attention:  Philip J. Niehoff, Esq.
                      Fax:  (312) 701-7711

     Notice shall be effective and deemed to have been received (i) when
delivered in person, (ii) when sent by fax with receipt acknowledged, (iii) five
(5) days after having been mailed by certified or registered United States mail,
postage prepaid, return receipt requested, or (iv) the next business day after
having been sent by a nationally recognized overnight mail or courier service,
receipt 

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requested.

          (b) CHANGES AND MODIFICATIONS; TERMINATION; ACTION UNDER THIS
AGREEMENT.  This Agreement may be terminated, changed, modified or extended, and
consents hereunder may be granted, only by an agreement in writing signed by
SCPG and the owners of a majority of the Common Shares owned by the Other
Holders.

          (c) COMPLETE AGREEMENT.  This Agreement embodies the complete 
agreement and understanding among the parties and supersedes and preempts any 
prior understandings, agreements, or representations by or among the parties, 
written or oral, which may have related to the subject matter hereof in any 
way. This Agreement shall be binding upon and inure to the benefit of the 
parties hereto and their respective successors and assigns (including, 
without limitation, successor holders of Shares); PROVIDED, HOWEVER, that 
SCPG may not assign or transfer its rights or obligations hereunder without 
the prior written consent of the owners of a majority of the Common Shares 
held by the Other Holders, except to one or more Persons of the types 
specified in Section 8.2 of the Purchase Agreement.

          (d) COUNTERPARTS.  This Agreement may be executed in counterparts,
each of which shall be deemed an original, but all of which taken together shall
constitute one instrument.

          (e) SEVERABILITY.  If in any judicial proceeding a court shall refuse
to enforce any provision of this Agreement, then such unenforceable provision
shall be deemed eliminated from this Agreement for the purpose of such
proceeding to the extent necessary to permit the remaining provisions to be
enforced.

          (f) GOVERNING LAW.  This Agreement shall be governed by the laws of
the State of Maryland without giving effect to the conflict of laws rules of any
jurisdiction.

          (g) REMEDIES.  The parties hereto shall have all remedies for breach
of this Agreement available to them provided by law or equity.  Without limiting
the generality of the foregoing, the parties agree that in addition to all other
rights and remedies available at law or in equity, the parties shall be entitled
to obtain specific performance of the obligations of each party to this
Agreement and immediate injunctive relief, and that in the event any action or
proceeding is brought in defense, that there is an inadequate remedy at law.

          (h) TRANSFERS.  It shall be a condition to any Transfer of Common
Shares to Affiliates of Michael W. Reschke that the Transferee agree in writing
to be bound by the obligations of the Other Holders pursuant to, and as provided
in, this Agreement, whereupon such Transferee shall be deemed to be a successor
in interest of the Other Holders for all purposes of this Agreement (but which
subsequent agreement shall not relieve the Other Holders of their obligations
hereunder).  Any Transfer in violation of this provision shall be void.

          (i) TERMINATION.  This Agreement shall terminate on the date on which
SCPG shall 

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cease to own Common Shares issued or issuable upon conversion or exchange of the
Preferred Shares representing at least five percent of the then outstanding
Common Shares (on a fully diluted basis).


                              [Signature Page Follows]


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          IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date set forth above.

                                       /s/   Michael W. Reschke
                                             ----------------------------------
                                             Michael W. Reschke


                               PRIME GROUP REALTY TRUST

                               By:   /s/ W. Michael Karnes
                                     ---------------------------------------
                               Its:  EXECUTIVE VP AND CHIEF FINANCIAL OFFICER


                               PRIME GROUP REALTY, L.P.

                               By:   Prime Group Realty Trust, its
                                     managing general partner

                               By:   /s/ W. Michael Karnes
                                     ----------------------------------------
                               Its:  Executive VP And Chief Financial Officer
                                     ----------------------------------------


                               PRIME GROUP II, L.P., PRIME GROUP
                               III, L.P., PRIME GROUP IV, L.P.,

                               PRIME GROUP V, L.P.

                               By:   PGLP, Inc., its sole General
                                     Partner

                               By:   /s/ Robert J. Rudnik
                                     ----------------------------------------
                               Its:  Vice President
                                     ----------------------------------------


                               PRIME GROUP LIMITED PARTNERSHIP

                               /S/   Michael W. Reschke                       
                                     ----------------------------------------
                               By:   Michael W. Reschke, its
                                     Managing General Partner


                               PRIME FINANCING, L.P.

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<PAGE>

                               By:   Prime Financing, Inc., its sole
                                     General Partner

                               THE PRIME GROUP, INC.

                               By:   /s/ Robert J. Rudnik
                                     ----------------------------------------
                               Its:  Vice President       


                               PG/PRIMESTONE, L.L.C.
                               By:   The Prime Group, Inc.,
                                     its Administrative Member

                               By:   /s/Robert J. Rudnik       
                                     ----------------------------------------
                               Its:  Vice President      


                               SECURITY CAPITAL PREFERRED
                               GROWTH INCORPORATED

                               By:   /s/ David Rosenbaum            
                                     ----------------------------------------
                               Its:  Vice President 


ACCEPTED AND AGREED TO
WITH RESPECT TO SECTION 2(d)(ii):

PRIME GROUP REALTY, L.P.

By:  Prime Group Realty Trust, its
     managing general partner


By:    /s/ W. Michael Karnes 
       -----------------------------------------
Name:  W. Michael Karnes   
       -----------------------------------------
Its:   Executive VP and Chief Financial Officer
       -----------------------------------------

PRIME GROUP REALTY TRUST

By:    /s/ W. Michael Karnes                    
       -----------------------------------------
Name:  W. Michael Karnes          
       -----------------------------------------
Its:   Executive VP and Chief Financial Officer
       -----------------------------------------

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