<PAGE>

                                                                    Exhibit 3.37

                    AMENDMENT NO. 32 TO AMENDED AND RESTATED
                        AGREEMENT OF LIMITED PARTNERSHIP
                           OF PRIME GROUP REALTY, L.P.

         This AMENDMENT NO. 32 TO AMENDED AND RESTATED AGREEMENT OF LIMITED
PARTNERSHIP OF PRIME GROUP REALTY, L.P. (this "Amendment") is made as of
December 30, 1999, by Prime Group Realty Trust, a Maryland real estate
investment trust ("PGRT"), as the Managing General Partner of Prime Group
Realty, L.P., a Delaware limited partnership (the "Partnership"), and on behalf
of the other Partners (as hereinafter defined). Capitalized terms used but not
otherwise defined herein shall have the meanings given to such terms in the
Amended and Restated Agreement of Limited Partnership of the Partnership, dated
as of November 17, 1997, by and among PGRT and the other parties signatory
thereto, as amended thereafter (as so amended, the "Limited Partnership
Agreement").

                              W I T N E S S E T H:

         WHEREAS, pursuant to Section 4.3.C. of the Limited Partnership
Agreement, the Managing General Partner may raise all or any portion of
Additional Funds required by the Partnership for the acquisition of additional
properties by accepting additional Capital Contributions, including the issuance
of Common Units for Capital Contributions that consist of property or interests
in property;

         WHEREAS, pursuant to that Real Estate Sales Contract, dated as of
October 20, 1997, by and among The Prime Group, Inc., an Illinois corporation,
Prime Group Realty Trust, a Maryland real estate investment trust, Prime Group
Realty, L.P., a Delaware limited partnership and the Contributors named therein
(the "Agreement"), the Partnership agreed to purchase the Vacant Parcels 4 and
11 in Carol Stream Industrial Business Park, Carol Stream, Illinois (the
"Property") upon the fulfillment of certain conditions;

         WHEREAS, the conditions of the Agreement having been fulfilled, the
Partnership is acquiring the Property in return for issuing Common Units of
Limited Partner Interest to Carol Stream Industrial Park Joint Venture; and

         WHEREAS, Sections 2.4 and 12.3 of the Limited Partnership Agreement
authorize, among other things, the Managing General Partner, as true and lawful
agent and attorney-in fact, to execute, swear to, acknowledge, deliver, file and
record this Amendment on behalf of each Partner that has executed the Limited
Partnership Agreement and on behalf of the Partnership.

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

         Section 1. ACCEPTANCE OF CAPITAL CONTRIBUTION IN EXCHANGE FOR COMMON
UNITS. (a) PGRT, as Managing General Partner and on behalf of the Partnership,
hereby accepts from Carol


<PAGE>


Stream Industrial Park Joint Venture the grant of all of its right, title and
interest in the Property, a legal description of which is attached hereto as
EXHIBIT 1, as a Capital Contribution in exchange for 151,621 Common Units of
Limited Partner Interest which are hereby issued by the Partnership to Carol
Stream Industrial Park Joint Venture pursuant to Section 4.3.C of the Limited
Partnership Agreement, and which are evidenced by Common Unit Certificate No. 58
of the Partnership.

                  (b) Each of the Common Units of Limited Partner Interest
issued to Carol Stream Industrial Park Joint Venture pursuant to this SECTION 2
shall have the same terms and provisions as the Common Units of Limited Partner
Interest issued by the Partnership on November 17, 1997 except that the Exchange
Rights relating thereto may be exercised only after the first (1st) anniversary
of their issuance (as opposed to November 17, 1998).

         Section 2. AMENDMENT OF EXHIBIT A TO THE LIMITED PARTNERSHIP AGREEMENT.
Exhibit A to the Limited Partnership Agreement is hereby amended and restated to
reflect the aforementioned change(s) by deleting Exhibit A attached thereto in
its entirety, and by attaching in lieu thereof a replacement exhibit in the form
of EXHIBIT A attached hereto. From and after the effectiveness of this
Amendment, the amended and restated EXHIBIT A attached hereto shall be the only
EXHIBIT A to the Limited Partnership Agreement, unless and until it is hereafter
further amended.

         Section 3. REFERENCE TO AND EFFECT ON THE LIMITED PARTNERSHIP
AGREEMENT.

                  A. The Limited Partnership Agreement is hereby deemed to be
amended to the extent necessary to effect the matters contemplated by this
Amendment. Except as specifically provided for hereinabove, the provisions of
the Limited Partnership Agreement shall remain in full force and effect.

                  B. The execution, delivery and effectiveness of this Amendment
shall not operate (i) as a waiver of any provision, right or obligation of the
Managing General Partner, the other General Partner or any Limited Partner under
the Limited Partnership Agreement except as specifically set forth herein or
(ii) as a waiver or consent to any subsequent action or transaction.

         Section 4. APPLICABLE LAW. This Amendment shall be construed in
accordance with and governed by the laws of the State of Delaware, without
regard to the principles of conflicts of law.

                            [signature page follows]


                                      -2-
<PAGE>


                                        AMENDMENT NO. 32 TO AMENDED AND
                                        RESTATED AGREEMENT OF LIMITED
                                        PARTNERSHIP OF PRIME GROUP REALTY, L.P.

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

                               MANAGING GENERAL PARTNER:

                               PRIME GROUP REALTY TRUST, a
                               Maryland real estate investment trust

                               By:_________________________

                               Name: ______________________

                               Title:________________________

                               LIMITED PARTNERS:

                               Each Limited Partner hereby executes
                               this Amendment to the Limited
                               Partnership Agreement.

                               By:      PRIME GROUP REALTY TRUST, a
                                        Maryland real estate investment
                                        trust, as attorney-in fact

                                        By:__________________________

                                        Name: _______________________

                                        Title:_________________________


                                      -3-
<PAGE>


As to Section 1 hereof,

ACKNOWLEDGED AND AGREED

CAROL STREAM INDUSTRIAL PARK JOINT
VENTURE, an Illinois general partnership

By:      NARCO ENTERPRISES, INC.,
         an Illinois corporation
         Its Managing General Partner

         By:   ______________________________
                           Stephen J. Nardi
                           President


                                      -4-
<PAGE>


                                   EXHIBIT A*

               PARTNERS, NUMBER OF UNITS AND CAPITAL CONTRIBUTIONS
<TABLE>
<CAPTION>
                                                   Number of         Capital
Managing General Partner                         Common Units      Contribution
<S>                                               <C>               <C>
Prime Group Realty Trust                          15,189,438           **
         77 West Wacker Drive
         Suite 3900
         Chicago, IL  60601
         Attn:  Richard S. Curto
                James F. Hoffman

GENERAL PARTNER

The Nardi Group, L.L.C.                             927,100          $18,542,000
         c/o Stephen J. Nardi
         4100 Madison Street
         Hillside, IL  60162

LIMITED PARTNERS

The Nardi Group, L.L.C.                             328,182           $4,906,061
         c/o Stephen J. Nardi
         4100 Madison Street
         Hillside, IL  60162

Carol Stream Industrial Park Joint Venture          151,621           $2,146,374
         c/o Stephen J. Nardi
         4100 Madison Street
         Hillside, IL  60162

Edward S. Hadesman
Trust Dated May 22, 1992                            398,427           $7,968,540
         c/o Edward S. Hadesman
         2500 North Lakeview
         Unit 1401
         Chicago, IL  60614
</TABLE>

--------------------------
* As amended by Amendment No. 32 to the Amended and Restated Agreement of
Limited Partnership of Prime Group Realty, L.P.

** This amount shall be inserted by the Managing General Partner.


                                   EXHIBIT A-1
<PAGE>

<TABLE>
<CAPTION>
                                                  Number of          Capital
Limited Partners                                Common Units       Contribution
<S>                                                <C>               <C>
Carolyn B. Hadesman                                54,544            $1,090,880
Trust Dated May 21, 1992
         c/o Edward S. Hadesman
         2500 North Lakeview
         Unit 1401
         Chicago, IL  60614

Lisa Hadesman 1991 Trust                           169,053           $3,381,060
         c/o Edward S. Hadesman
         2500 North Lakeview
         Unit 1401
         Chicago, IL  60614

Cynthia Hadesman 1991 Trust                        169,053           $3,381,060
         c/o Edward S. Hadesman
         2500 North Lakeview
         Unit 1401
         Chicago, IL  60614

Tucker B. Magid                                     33,085             $661,700
         545 Ridge Road
         Highland Park, IL 60035

Frances S. Shubert                                  36,006             $720,120
         511 Lynn Terrace
         Waukegan, IL  60085

Sky Harbor Associates                               62,149           $1,242,980
         c/o Howard I. Bernstein
         6541 North Kilbourn
         Lincolnwood, IL  60646

Jeffrey A. Patterson                               110,000           $2,200,000
         c/o Prime Group Realty Trust
         77 West Wacker Drive
         Suite 3900
         Chicago, IL  60601
</TABLE>


                                   EXHIBIT A-2
<PAGE>

<TABLE>
<CAPTION>
                                                   Number of         Capital
Limited Partners                                 Common Units      Contribution

<S>                                                 <C>             <C>
Primestone Investment Partners, L.P.                7,944,893         **
         c/o The Prime Group, Inc.
         77 West Wacker Drive
         Suite 4200
         Chicago, IL 60601
         Attn:  Paul A. Roehri

Prime Group VI, L.P.                                  304,097         $6,050,500
         c/o The Prime Group, Inc.
         77 West Wacker Drive
         Suite 4200
         Chicago, IL 60601
         Attn:  Michael W. Reshcke
                Robert J. Rudnik

H Group LLC                                            93,849         $1,400,000
         c/o Heitman Financial Ltd.
         180 N. LaSalle
         Suite 3600
         Chicago, IL 60601
         Attn:  Norman Perlmutter

Ray R. Grinvalds                                        2,608            $52,160
         714 Blaine Court
         Schaumburg, IL 60173

Sandra F. Grinvalds                                     2,608            $52,160
         714 Blaine Court
         Schaumburg, IL 60173

Warren H. John, as Trustee of the Warren H. John       37,259           $745,180
Trust dated December 18, 1998
         1730 N. Clark Street
         Chicago, IL 60614
</TABLE>

--------------------------
** This amount shall be inserted by the Managing General Partner.


                                   EXHIBIT A-3
<PAGE>


<TABLE>
<CAPTION>
                                            Number of                       Capital
Managing General Partner                 Preferred Units                 Contribution

<S>                                      <C>                             <C>
Prime Group Realty Trust                 2,000,000                                 **
         77 West Wacker Drive            Convertible Preferred
         Suite 3900                      Units
         Chicago, IL  60601
         Attn:    Richard S. Curto
                  James F. Hoffman

Prime Group Realty Trust                 4,000,000                                **/
         77 West Wacker Drive            Series B Preferred Units
         Suite 3900
         Chicago, IL  60601
         Attn:    Richard S. Curto
                  James F. Hoffman
</TABLE>

----------------------
** This amount shall be inserted by the Managing General Partner.


                                   EXHIBIT A-4