<PAGE>   1

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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                              ---------------------
                                    FORM 10-Q


          [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                        SECURITIES EXCHANGE ACT OF 1934


                FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1998


          [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                        SECURITIES EXCHANGE ACT OF 1934

                         COMMISSION FILE NUMBER: 1-10643

                              ---------------------


                         HALLWOOD REALTY PARTNERS, L.P.
             (Exact name of registrant as specified in its charter)


                             -----------------------


                DELAWARE                                      75-2313955
     (State or other jurisdiction of                       (I.R.S. Employer
      incorporation or organization)                    Identification Number)


              3710 RAWLINS
               SUITE 1500
              DALLAS, TEXAS                                   75219-4298
(Address of principal executive offices)                      (Zip Code)


       Registrant's telephone number, including area code: (214) 528-5588


Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

                                Yes  X   No
                                   ----    ----

            THE REGISTRANT IS A LIMITED PARTNERSHIP AND ISSUES UNITS
              REPRESENTING OWNERSHIP OF LIMITED PARTNER INTERESTS.

        NUMBER OF UNITS OUTSTANDING AT NOVEMBER 2, 1998: 1,672,556 UNITS.




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                                     Page 1

<PAGE>   2




                         HALLWOOD REALTY PARTNERS, L.P.

                                    FORM 10-Q

                                TABLE OF CONTENTS


<TABLE>
<CAPTION>

PART I - FINANCIAL INFORMATION
                                                                                                Page
                                                                                                ----
<S>                                                                                             <C>
Item 1          Financial Statements (unaudited) :

                Consolidated Balance Sheets as of September 30, 1998
                and December 31, 1997                                                            3

                Consolidated Statements of Income for the
                Three and Nine Months Ended September 30, 1998 and 1997                          4

                Consolidated Statements of Cash Flows for the
                Nine Months Ended September 30, 1998 and 1997                                    5

                Notes to Consolidated Financial Statements                                       6

Item 2          Management's Discussion and Analysis of Financial Condition
                and Results of Operations, Liquidity and Capital Resources                       9


PART II - OTHER INFORMATION


Items 1 to 6    Other Information                                                               12

                Signatures                                                                      13

</TABLE>



                                     Page 2

<PAGE>   3




                         HALLWOOD REALTY PARTNERS, L.P.
                           CONSOLIDATED BALANCE SHEETS
                       (IN THOUSANDS EXCEPT UNIT AMOUNTS)


<TABLE>
<CAPTION>

                                                         SEPTEMBER 30,  December 31,
                                                             1998          1997
                                                         ------------   ------------
                                                          (UNAUDITED)
<S>                                                       <C>           <C>
ASSETS

Real estate:
    Land                                                  $   56,441    $   56,441
    Buildings and improvements                               260,488       259,220
    Tenant improvements                                       18,210        18,734
                                                          ----------    ----------
                                                             335,139       334,395
    Accumulated depreciation and amortization               (160,098)     (155,367)
                                                          ----------    ----------
       Real estate, net                                      175,041       179,028

Cash and cash equivalents                                     13,621         6,665
Accounts receivable                                            1,394         1,162
Deferred lease commissions, net                                7,114         7,049
Lease concessions                                              2,811         2,511
Loan reserves and escrows                                      7,174         6,215
Loan costs, net                                                3,801         3,213
Prepaid expenses and other assets, net                         1,024         1,291
                                                          ----------    ----------

       Total assets                                       $  211,980    $  207,134
                                                          ==========    ==========



LIABILITIES AND PARTNERS' CAPITAL

Liabilities:
    Mortgages payable                                     $  162,207    $  157,911
    Unamortized mortgage payable forgiveness                   7,657         8,926
    Accounts payable and accrued expenses                      3,389         4,157
    Prepaid rent and security deposits                         2,807         2,764
    Payable to affiliates                                        304           335
                                                          ----------    ----------
       Total liabilities                                     176,364       174,093
                                                          ----------    ----------
Partners' capital:
    Limited partners - 1,672,556 units outstanding            35,260        32,711
    General partner                                              356           330
                                                          ----------    ----------
       Total partners' capital                                35,616        33,041
                                                          ----------    ----------

       Total liabilities and partners' capital            $  211,980    $  207,134
                                                          ==========    ==========


</TABLE>




                 See notes to consolidated financial statements.





                                     Page 3

<PAGE>   4




                         HALLWOOD REALTY PARTNERS, L.P.
                        CONSOLIDATED STATEMENTS OF INCOME
                     (IN THOUSANDS EXCEPT PER UNIT AMOUNTS)
                                   (UNAUDITED)

<TABLE>
<CAPTION>


                                                THREE MONTHS ENDED       NINE MONTHS ENDED
                                                   SEPTEMBER 30,           SEPTEMBER 30,
                                               ---------------------   ----------------------
                                                 1998        1997        1998         1997
                                               ---------   ---------   ---------    ---------
<S>                                            <C>         <C>         <C>          <C>      
REVENUES:
   Property operations                         $  14,275   $  13,391   $  41,503    $  39,476
   Interest                                          240         142         606          408
                                               ---------   ---------   ---------    ---------
      Total revenues                              14,515      13,533      42,109       39,884
                                               ---------   ---------   ---------    ---------

EXPENSES:
   Property operations                             5,858       5,843      16,599       17,072
   Interest                                        3,193       3,254       9,511        9,710
   Depreciation and amortization                   2,994       3,012       9,082        9,007
   General and administrative                        743         855       2,466        2,522
                                               ---------   ---------   ---------    ---------
      Total expenses                              12,788      12,964      37,658       38,311
                                               ---------   ---------   ---------    ---------

INCOME BEFORE EXTRAORDINARY ITEM                   1,727         569       4,451        1,573

Extraordinary item -
   Loss on early extinguishment of debt               --          --      (1,876)          --
                                               ---------   ---------   ---------    ---------

NET INCOME                                     $   1,727   $     569   $   2,575    $   1,573
                                               =========   =========   =========    =========

ALLOCATION OF NET INCOME:
   Limited partners                            $   1,710   $     563   $   2,549    $   1,557
   General partner                                    17           6          26           16
                                               ---------   ---------   ---------    ---------
      Total                                    $   1,727   $     569   $   2,575    $   1,573
                                               =========   =========   =========    =========

NET INCOME PER UNIT AND
POTENTIAL UNIT:
   Earnings per unit - basic
      Income before extraordinary item         $    1.02   $     .34   $    2.63    $     .93
      Loss on early extinguishment of debt            --          --       (1.11)          --
                                               ---------   ---------   ---------    ---------
          Net income                           $    1.02   $     .34   $    1.52    $     .93
                                               =========   =========   =========    =========

   Earnings per unit - assuming dilution
      Income before extraordinary item         $     .98   $     .33   $    2.53    $     .90
      Loss on early extinguishment of debt            --          --       (1.07)          --
                                               ---------   ---------   ---------    ---------
          Net income                           $     .98   $     .33   $    1.46    $     .90
                                               =========   =========   =========    =========

WEIGHTED AVERAGE UNITS USED IN
COMPUTING NET INCOME PER UNIT AND
POTENTIAL UNIT:
   Basic                                           1,673       1,673       1,673        1,673
                                               =========   =========   =========    =========
   Assuming dilution                               1,743       1,730       1,741        1,724
                                               =========   =========   =========    =========
</TABLE>


                 See notes to consolidated financial statements.


                                     Page 4

<PAGE>   5




                         HALLWOOD REALTY PARTNERS, L.P.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
                                   (UNAUDITED)


<TABLE>
<CAPTION>

                                                                        NINE MONTHS ENDED
                                                                           SEPTEMBER 30,
                                                                     ------------------------
                                                                        1998          1997
                                                                     ----------    ----------
<S>                                                                  <C>           <C>       
OPERATING ACTIVITIES:
   Net income                                                        $    2,575    $    1,573
   Adjustments to reconcile net income
   to net cash provided by operating activities:
      Depreciation and amortization                                       9,082         9,007
      Loss on early extinguishment of debt                                1,876            --
      Amortization of mortgage principal forgiveness                     (1,269)       (1,250)
      Lease concessions                                                    (300)          (15)
   Changes in assets and liabilities:
      Receivables                                                          (232)          245
      Prepaid lease commissions                                          (1,734)       (1,668)
      Prepaid expenses and other assets, net                                176           878
      Accounts payable and other liabilities                               (756)       (2,030)
                                                                     ----------    ----------
         Net cash provided by operating activities                        9,418         6,740
                                                                     ----------    ----------

INVESTING ACTIVITIES:
   Property and tenant improvements                                      (3,403)       (3,744)
   Tenant improvement escrow                                                 --           645
   Property acquisition                                                      --          (649)
   Mortgage receivable principal payments                                    --            46
                                                                     ----------    ----------
         Net cash used for investing activities                          (3,403)       (3,702)
                                                                     ----------    ----------

FINANCING ACTIVITIES:
   Mortgage principal proceeds                                           41,500           549
   Mortgage principal refinanced                                        (35,046)           --
   Mortgage prepayment penalties                                         (1,655)           --
   Mortgage principal payments                                           (2,158)       (2,403)
   Loan reserves                                                           (550)           --
   Loan fees                                                             (1,150)           25
                                                                     ----------    ----------
         Net cash provided by (used for) financing activities               941        (1,829)
                                                                     ----------    ----------

INCREASE IN CASH AND CASH EQUIVALENTS                                     6,956         1,209
BEGINNING CASH AND CASH EQUIVALENTS                                       6,665         3,556
                                                                     ----------    ----------
ENDING CASH AND CASH EQUIVALENTS                                     $   13,621    $    4,765
                                                                     ==========    ==========




           SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:

                   Interest paid in cash during the period           $   10,399    $   10,654
                                                                     ==========    ==========
</TABLE>



                 See notes to consolidated financial statements.

                                     Page 5

<PAGE>   6



                         HALLWOOD REALTY PARTNERS, L.P.
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                  FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1998
                                   (UNAUDITED)


1   ORGANIZATION AND ACCOUNTING POLICIES

    Hallwood Realty Partners, L.P. ("HRP"), a publicly traded Delaware limited
    partnership, is engaged in diversified real estate activities, including the
    acquisition, ownership and operation of commercial office and industrial
    real estate and other real estate related assets. Limited partners'
    interests are traded on the American Stock Exchange under the symbol "HRY".

    Hallwood Realty Corporation ("HRC" or "General Partner"), a Delaware
    corporation and wholly-owned subsidiary of The Hallwood Group Incorporated
    ("Hallwood"), is HRP's general partner and is responsible for asset
    management of the partnership and its real estate properties. Hallwood
    Commercial Real Estate, Inc. ("HCRE"), another wholly-owned subsidiary of
    Hallwood, provides property management services for HRP's real estate
    properties.

    HRP has adopted Statements of Financial Accounting Standards ("SFAS") No.
    130 "Reporting on Comprehensive Income" effective January 1, 1998. As HRP
    had no items of other comprehensive income in the periods presented.

    SFAS No. 131 "Disclosures about Segments of an Enterprise and Related
    Information" redefines how operating segments are determined and requires
    disclosure of certain financial and descriptive information about a
    company's operating segments. It establishes standards for reporting and
    displaying information about operating segments in annual financial
    statements and requires that enterprises report selected information about
    operating segments in interim reports. HRP will adopt the statement during
    the fourth quarter of 1998 and does not expect it to have a material impact
    on its financial condition or results of operations, although additional
    disclosure may be required.

    In June 1998, SFAS No. 133 "Accounting for Derivative Instruments and
    Hedging Activities" was issued, which establishes standards for and
    disclosures of derivative instruments and hedging activities. HRP currently
    has no derivative instruments in place.

    The accompanying unaudited consolidated financial statements have been
    prepared in accordance generally accepted accounting principles and with the
    instructions to Form 10-Q. These financial statements should be read in
    conjunction with the audited consolidated financial statements and related
    disclosures thereto included in Form 10-K for the year ended December 31,
    1997. In the opinion of management, all adjustments considered necessary for
    a fair presentation have been included. Operating results for the nine
    months ended September 30, 1998 are not necessarily indicative of the
    results that may be expected for the year ending December 31, 1998.


2   TRANSACTIONS WITH RELATED PARTIES

    HRC and HCRE are compensated for services provided to HRP and its real
    estate properties and are set forth in the following table for the periods
    presented (in thousands):

<TABLE>
<CAPTION>

                                       ENTITY             THREE MONTHS              NINE MONTHS
                                      PAID OR                ENDED                     ENDED
                                     REIMBURSED           SEPTEMBER 30,             SEPTEMBER 30,
                                     ----------         -----------------         ----------------
                                                        1998         1997         1998        1997
                                                        ----         ----         ----        ----
<S>                                  <C>               <C>          <C>        <C>         <C>    
    Asset management fee                 HRC           $ 125        $ 119      $   369     $   340
    Property management fee             HCRE             411          387        1,198       1,135
    Lease commissions                   HCRE             276          372        1,312       1,181
    Construction fees                   HCRE              93           89          198         238
    Acquisition fee                      HRC               -            -            -           7
    Reimbursements of costs (a)          HRC             523          511        1,681       1,725
</TABLE>


(a) These costs are mostly recorded as general and administrative expenses and
    represent reimbursement to HRC, at cost, for partnership level salaries,
    employee and director insurance, and certain overhead costs. HRP pays, on a
    monthly basis, the balance of its account with HRC.



                                     Page 6

<PAGE>   7



                         HALLWOOD REALTY PARTNERS, L.P.
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                  FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1998
                                   (UNAUDITED)


3   MORTGAGES PAYABLE

    On February 27, 1998, HRP entered into an agreement to refinance the
    mortgage loan secured by Executive Park that became effective March 20,
    1998. The new loan reduces the interest rate from 8.87% to an effective
    interest rate of 7.32% and extends the amortization period from fifteen
    years to approximately twenty-seven years with a maturity date of April 11,
    2008. The loan proceeds of $34,000,000 were used (i) to pay the outstanding
    principal balance of $28,707,000 with the former lender, (ii) to pay
    transaction costs of approximately $894,000, (iii) to pay a prepayment
    penalty of $1,465,000, (iv) to pay $550,000 of net loan reserves, and (v)
    for general working capital. The prepayment penalty along with the write off
    of $146,000 of unamortized loan costs associated with the retired loan were
    expensed and are included in the Statements of Income as an extraordinary
    item as a loss on early extinguishment of debt.

    On June 1, 1998, HRP refinanced the mortgage loan secured by Seattle
    Business Parks into two new loans which reduced the interest rate from 9.25%
    to 6.97%. The new loans lengthen the amortization period from twenty-two
    years to thirty years and the maturity date was extended by seven years to
    June 7, 2008. The loan proceeds of $7,500,000 were used (i) to pay the
    outstanding principal balance of $6,339,000 with the former lender, (ii) to
    pay transaction costs of approximately $228,000, (iii) to pay a prepayment
    penalty of $190,000, and (iv) for general working capital. The prepayment
    penalty along with the write off of $75,000 of unamortized loan costs
    associated with the retired loan were expensed and are included in the
    Statements of Income as an extraordinary item as a loss on early
    extinguishment of debt.


4   EARNINGS PER UNIT

    Basic earnings per unit is computed by dividing net income attributable to
    the limited partners' interests by the weighted average number of units
    outstanding. Earnings per unit assuming dilution is computed by dividing net
    income attributable to the limited partners' interests by the weighted
    average number of units and potential units outstanding. Options to acquire
    units were issued during 1995 and are considered to be potential units. The
    number of potential units is computed using the treasury stock method which
    assumes that the increase in the number of units is reduced by the number of
    units which could have been repurchased by HRP with the proceeds from the
    exercise of these options. The following table illustrates the amounts used
    to calculate the weighted average number of units outstanding:

<TABLE>
<CAPTION>

                                                             THREE MONTHS       NINE MONTHS
                                                                ENDED               ENDED
                                                             SEPTEMBER 30,       SEPTEMBER 30,
                                                           ----------------    ----------------
                                                            1998      1997      1998      1997
                                                           ------    ------    ------    ------
<S>                                                         <C>       <C>       <C>       <C>  
Weighted average units outstanding - basic                  1,673     1,673     1,673     1,673

Issuance of units from options                                 86        86        86        86

Repurchase of units from unit option proceeds                 (16)      (29)      (18)      (35)
                                                           ------    ------    ------    ------
Weighted average units outstanding - assuming dilution      1,743     1,730     1,741     1,724
                                                           ======    ======    ======    ======
</TABLE>





                                     Page 7

<PAGE>   8



                         HALLWOOD REALTY PARTNERS, L.P.
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                  FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1998
                                   (UNAUDITED)


5   LITIGATION

    Reference is made to Note 9 to the audited consolidated financial statements
    contained in Form 10-K for the year ended December 31, 1997. Beginning in
    1997, HRP has been involved in two lawsuits with Gotham Partners, L.P. The
    first complaint seeks access to certain books and records of HRP, a list of
    the limited partners and reimbursement of the plaintiff's expenses. The
    second complaint alleges claims of breach of fiduciary duties, breach of
    HRP's partnership agreement, fraud, and as to Hallwood, aiding and abetting
    these alleged breaches.

    On June 27, 1997, the parties entered into a Stipulation and Order under
    which HRP provided to plaintiff copies of certain of the documents
    requested. The other claims in the two actions remain outstanding.

    On August 27, 1997, defendants moved to dismiss the complaint in the second
    action for plaintiff's failure either to make a demand on the general
    partner to bring suit or to allege adequately that such a demand was futile.
    On February 6, 1998, the Court granted defendants' motion to dismiss but
    gave plaintiff thirty days to file an amended complaint. Plaintiffs filed an
    amended complaint on March 6, 1998, which defendants have again moved to
    dismiss.

    HRP's management believes that the claims are without merit and intend to
    defend the cases vigorously, but because of their early stages, cannot
    predict the outcome of the claims or any possible effect an adverse outcome
    might have.









                                     Page 8

<PAGE>   9


                         HALLWOOD REALTY PARTNERS, L.P.



ITEM 2.    MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
           RESULTS OF OPERATIONS, LIQUIDITY AND CAPITAL RESOURCES


RESULTS OF OPERATIONS

THIRD QUARTER OF 1998 COMPARED TO THE THIRD QUARTER OF 1997

REVENUE FROM PROPERTY OPERATIONS increased $884,000, or 6.6%, for the third
quarter of 1998, compared to the 1997 third quarter. The following table
illustrates the components of the change, in thousands:

<TABLE>

<S>                                               <C>    
               Rental income, net                 $ 683  
               Expense recoveries                   150  
               Other property income                 51  
                                                  -----  
                  Net increase                    $ 884  
                                                  =====  
</TABLE>


Although average occupancy between the comparable periods increased slightly
from 93.4% to 93.5%, rental income increased due to rental rate increases at a
number of properties, with the largest gains at Executive Park and Parklane
Towers. As of September 30, 1998, HRP had leases executed and in place for 94.1%
of the portfolio's net rentable square feet.

INTEREST INCOME increased $98,000 as a result of additional earnings on
overnight investments due to higher average cash balances available for
investment between the periods.

PROPERTY OPERATING EXPENSES increased $15,000 for the third quarter of 1998,
compared to the same period in 1997, primarily due to a net increase in several
types of costs, none of which are individually significant.

INTEREST EXPENSE diminished $61,000, or 1.9%, due to (i) lower principal
balances as a result of scheduled principal payments and (ii) lower interest
rates from the refinancing of loans secured by Executive Park and Seattle
Business Parks during 1998 (see Note 3 to the consolidated financial
statements).

DEPRECIATION AND AMORTIZATION EXPENSE was consistent between the periods.

GENERAL AND ADMINISTRATIVE EXPENSES decreased $112,000 for the third quarter of
1998, as compared to the 1997 period, primarily due to lower investor mailing
costs and certain professional fees, partially offset by an increase in state
franchise taxes in Michigan.


FIRST NINE MONTHS OF 1998 COMPARED TO THE FIRST NINE MONTHS OF 1997

REVENUE FROM PROPERTY OPERATIONS increased $2,027,000, or 5.1%, for the first
nine months of 1998, compared to the first nine months of 1997. The following
table illustrates the components of the change, in thousands:

<TABLE>

<S>                                               <C>     
               Rental income, net                 $ 1,998 
               Expense recoveries                   (138) 
               Other property income                  167 
                                                   ------ 
                  Net increase                    $ 2,027 
                                                   ====== 
</TABLE>


Rental income increased due to rental rate increases at a number of properties
(primarily at Executive Park and Corporate Square in the Atlanta market) and
also due to a rise in average occupancy between the comparable periods to 93.6%
from 92.8%. As of September 30, 1998, HRP had leases executed and in place for
94.1% of the portfolio's net rentable square feet.

INTEREST INCOME increased $198,000 as a result of additional earnings on
overnight investments due to higher average cash balances available for
investment between the periods.

                                     Page 9

<PAGE>   10


                         HALLWOOD REALTY PARTNERS, L.P.



RESULTS OF OPERATIONS - CONTINUED

PROPERTY OPERATING EXPENSES decreased $473,000, or 2.8%, for the first nine
months of 1998, compared to the same period in 1997. The decrease is comprised
of the following components:

    o     Real estate taxes decreased $511,000 primarily due to tax refunds
          received in 1998 for tax years 1994 to 1997 for Parklane Towers and
          Raintree Industrial Park.

    o     Management fees rose $92,000 due to the increase in occupancy and net
          rental income mentioned above.

    o     Janitorial costs increased $89,000 principally due to the increase in
          occupancy.

    o     Combined, all other operating costs decreased $143,000 between the
          periods.

INTEREST EXPENSE diminished $199,000, or 2.0%, due to (i) lower principal
balances as a result of scheduled principal payments and (ii) lower interest
rates from the refinancing of loans secured by Executive Park and Seattle
Business Parks during 1998 (see Note 3 to the consolidated financial
statements).

DEPRECIATION AND AMORTIZATION EXPENSE increased $75,000 primarily due to an
increase in lease commission amortization as a result of new leases executed
during 1997 which have increased the portfolio's occupancy.

GENERAL AND ADMINISTRATIVE EXPENSES decreased $56,000 for the first nine months
of 1998, as compared to the same period in 1997, due to lower insurance premiums
for director and officer coverage and lower investor mailing costs, partially
offset by an increase in state franchise taxes in Michigan.

LOSS ON EARLY EXTINGUISHMENT OF DEBT of $1,876,000 in the 1998 period represents
prepayment penalties of $1,655,000 incurred with the early payoff of loans
secured by Executive Park and Seattle Business Parks, along with the write off
of $221,000 of unamortized loan costs associated with the retired loans (see
Note 3 to the consolidated financial statements for more information about the
refinancing of the loans).


LIQUIDITY AND CAPITAL RESOURCES

HRP is engaged in diversified real estate activities, including the acquisition,
ownership and operation of commercial office and industrial real estate and
other real estate related assets. While it is the General Partner's primary
intention to operate HRP's existing real estate investments and to acquire and
operate additional real estate investments, HRC also continually evaluates each
of HRP's real estate investments in light of current economic trends and
operations to determine if any should be considered for disposal.

As of September 30, 1998, HRP owned twelve real estate properties located in six
states. Seven are commercial office building properties and five are industrial
park properties containing approximately 2,610,000 and 2,540,000 net rentable
square feet, respectively. HRP seeks to maximize the value of its real estate by
making capital and tenant improvements, by executing marketing programs to
attract and retain tenants, and reducing operating expenses where possible.

HRP's cash position increased $6,956,000 during the first nine months of 1998
from $6,665,000 as of December 31, 1997 to $13,621,000 as of September 30, 1998.
The sources of cash during the period were $41,500,000 of mortgage principal
proceeds and $9,418,000 of cash provided by operating activities. Uses of cash
during the period were $35,046,000 of mortgage principal repayments from
refinancing proceeds, $3,403,000 of property and tenant improvements, $1,655,000
of mortgage prepayment penalties, $2,158,000 of scheduled mortgage principal
payments, $1,150,000 of loan fees, and $550,000 of net loan reserve
requirements.

Each quarter HRC, as General Partner, reviews the Partnership's capacity to make
cash distributions. HRP has not made any cash distributions since February,
1992.

Substantially all of the buildings in eleven of HRP's real estate properties
were encumbered by and pledged as collateral under non-recourse mortgages as of
September 30, 1998. HRP has no mortgage loans maturing or requiring balloon
principal payments until the year 2003. Based upon loan amortizations in effect,
HRP is required to pay $713,000 of principal payments for the remainder of 1998.

                                     Page 10

<PAGE>   11


                         HALLWOOD REALTY PARTNERS, L.P.


LIQUIDITY AND CAPITAL RESOURCES - CONTINUED

HRP has incurred $3,403,000 of tenant and capital improvements and $1,734,000 of
lease commissions in the first nine months of 1998. Based on current information
available, management anticipates that the 1998 fourth quarter expenditures for
tenant and capital improvements will be approximately $1,300,000 and lease
commissions will be approximately $550,000. HRP believes that for the
foreseeable future, mortgage principal payments, tenant and capital
improvements, and lease commissions will be funded by net cash from operations.
The primary sources of capital to fund any future acquisitions will be proceeds
from the sale, financing or refinancing of one or more of its real estate
properties.

YEAR 2000 UPDATE -

HRP realizes that many of the world's information systems and/or computer
programs currently do not have the ability to recognize four digit date code
fields and accordingly, they do not have the ability to distinguish a year that
begins with "20" instead of the familiar "19". If not corrected, many computer
applications could fail, become unstable, stop working altogether, or create
erroneous or incorrect results. Therefore, many companies and organizations are
spending considerable resources to update and modify their systems for year 2000
compliance.

HRP developed a program to review and modify, where necessary, its computers,
computer programming and building systems to process transactions and/or operate
in the year 2000 and beyond. HRP has identified four of its primary systems
which are vulnerable to the year 2000 issue: (1) General Ledger/Accounts
Payable/Accounts Receivable Systems. These systems were modified by the vendor
at no cost to HRP during the third quarter of 1998 and are now year 2000
compliant. (2) Commercial Lease Administration. The system used by HRP is year
2000 compliant. (3) K-1 Processing. HRP maintains data used to process its
partners Schedule K-1(s) for tax reporting purposes in an environment that is
not year 2000 compliant. HRP has selected a tested and compliant system which
will be installed in 1999 at minimal cost. (4) Payroll. The General Partner
processes payroll in a non-compliant system through an outside payroll vendor.
Year 2000 compliant software has been purchased and will be installed in the
fourth quarter of 1998 at minimal cost.

Additionally, HRP is surveying all of its significant service providers and
other external parties to determine their compliance with the year 2000 issue
and what impact, if any, their efforts will have on HRP's business and
operations. HRP anticipates completing its survey of service providers and
vendors by January 1, 1999. HRP will utilize external and internal resources to
reprogram, replace and test its systems for year 2000 modifications. HRP
anticipates completing the year 2000 project by June 30, 1999. Total anticipated
costs are expected to be minimal and to be less than $50,000. In the event that
a system will not be year 2000 compliant, HRP will assess the potential risk
and, to the extent it is feasible, transfer its business to an alternate vendor.

Although HRP believes that it will not have any detrimental effects on its
operations from year 2000 compliance issues, there can be no assurance that the
systems of other companies, on which HRP's systems may rely, will be converted
timely, or converted in a manner that is compatible with HRP's systems, or that
any such failures by such other companies would not have a material adverse
effect or risk to HRP. HRP plans to devote all resources that would be required
to resolve any such issues in a timely manner that might arise from matters not
previously considered.

The cost of year 2000 compliance and the estimated date of completion of
necessary modifications are based on HRP's best estimates, which were derived
from various assumptions of future events, including the continued availability
of certain resources, third party modification plans and other factors. However,
there can be no guarantee that these estimates will be achieved and actual
results could differ materially from those anticipated.

FORWARD-LOOKING STATEMENTS -

This Form 10-Q contains certain forward-looking statements, which include the
plans and objectives of management for future operations. The forward-looking
statements included herein are based on current expectations that involve
numerous risks and uncertainties. Assumptions relating to the foregoing involve
judgments with respect to, among other things, future economic, competitive and
market conditions and future business decisions, all of which are difficult or
impossible to predict accurately and many of which are beyond the control of
HRP. Although HRP believes that the assumptions underlying the forward-looking
statements are reasonable, any of the assumptions could be inaccurate and,
therefore, there can be no assurance that the forward-looking statements will
prove to be accurate. In light of the significant uncertainties inherent in the
forward-looking statements included herein, the inclusion of such information
should not be regarded as a representation by HRP or any other person that the
objectives and plans of HRP will be achieved.

                                     Page 11

<PAGE>   12


                         HALLWOOD REALTY PARTNERS, L.P.




                           PART II - OTHER INFORMATION
<TABLE>
<CAPTION>

             Item
             ----

<S>          <C>        <C>                                                                      <C>
             1          Legal Proceedings                                                        None.

             2          Changes in Securities                                                    None.

             3          Defaults upon Senior Securities                                          None.

             4          Submission of Matters to a Vote of Security Holders                      None.

             5          Other Information                                                        None.

             6          Exhibits and Reports on Form 8-K

                        (a) Exhibits

                            The following exhibit is being filed as part of this Report:

                            Exhibit No.              Description

                            27                       Financial Data Schedule                     Page 14

                        (b) Reports on Form 8-K                                                  None.

</TABLE>


                                     Page 12

<PAGE>   13


                         HALLWOOD REALTY PARTNERS, L.P.


                                   SIGNATURES


Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.




                              HALLWOOD REALTY PARTNERS, L.P.
                              -------------------------------
                                        (Registrant)

                              By:  HALLWOOD REALTY CORPORATION
                                   General Partner



Date: November 4, 1998        By:  /s/ WILLIAM L. GUZZETTI
      ----------------             ---------------------------------------------
                                   William L. Guzzetti
                                   President
                                   (Chief Operating Officer)


Date: November 4, 1998        By:  /s/ JEFFREY D. GENT
      ----------------             ---------------------------------------------
                                   Jeffrey D. Gent
                                   Vice President - Finance
                                   (Principal Financial and Accounting Officer)









                                     Page 13

<PAGE>   14


                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>

Exhibit No.              Description
-----------              -----------
<S>                     <C>
    27                   Financial Data Schedule
</TABLE>