<PAGE>   1
                                   FORM 10-Q
                       SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549

                   QUARTERLY REPORT UNDER SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

               FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1998

                         COMMISSION FILE NUMBER 0-14457


                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
             (Exact name of registrant as specified in its charter)



            MARYLAND                                            52-1394972
  (State or other jurisdiction                               (I.R.S. Employer
of incorporation or organization)                           Identification No.)



                       9200 KEYSTONE CROSSING, SUITE 500
                        INDIANAPOLIS, INDIANA 46240-7602
                    (Address of principal executive offices)
                                   (Zip Code)


                                 (317) 817-7500
              (Registrant's telephone number, including area code)

                                 NOT APPLICABLE
              (Former name, former address and former fiscal year,
                         if changed since last report.)


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
    -----          -----
<PAGE>   2
PART 1 - FINANCIAL INFORMATION
ITEM 1 - FINANCIAL STATEMENTS

                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                        STATEMENTS OF FINANCIAL POSITION


<TABLE>
<CAPTION>
                                                                                            September 30,
                                                                                                 1998             December 31,
                                                                                             (Unaudited)              1997
                                                                                            -------------         ------------
                                     ASSETS
                                     ------
<S>                                                                                            <C>                   <C>
Cash and cash equivalents                                                                      $ 509,316             $ 538,513
Investments in and advances to Local Limited Partnerships (Note 2)                                73,200                87,108
                                                                                                --------              --------

                                                                                               $ 582,516             $ 625,621
                                                                                                ========              ========

                   LIABILITIES AND PARTNERS' EQUITY (DEFICIT)
                   ------------------------------------------

Liabilities:
    Administrative and reporting fee payable to General Partner (Note 3)                       $  64,686             $     -
    Accrued expenses                                                                              32,555                40,890
                                                                                                --------              --------

                                                                                                  97,241                40,890
                                                                                                --------              --------

Partners' equity (deficit):
   General Partner -- The National Housing Partnership (NHP)                                     (90,397)              (89,402)
   Original Limited Partner -- 1133 Fifteenth Street Three Associates                            (95,297)              (94,302)
   Other Limited Partners -- 11,500 investment units                                             670,969               768,435
                                                                                                --------              --------

                                                                                                 485,275               584,731
                                                                                                --------              --------

                                                                                               $ 582,516             $ 625,621
                                                                                                ========              ========
</TABLE>





                       See notes to financial statements.

                                      -1-
<PAGE>   3
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                            STATEMENTS OF OPERATIONS
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                                     Three Months Ended               Nine Months Ended
                                                                       September 30,                    September 30,
                                                                  -------------------------          -------------------------
                                                                    1998            1997               1998             1997
                                                                  -------         ---------          ---------        --------
<S>                                                               <C>           <C>                 <C>              <C>
REVENUES:
   Share of income from Local Limited Partnerships               $    -          $  357,860         $      -         $ 357,860
   Distributions and repayments received in excess
    of investment in Local Limited Partnerships                       -              16,310                -            32,008
   Interest income                                                  4,292             6,642             16,183           9,342
                                                                  -------         ---------          ---------        --------

                                                                    4,292           380,812             16,183         399,210
                                                                  -------        ----------          ---------        --------

COSTS AND EXPENSES:
   Administrative and reporting fees to
    General Partner (Note 3)                                       21,562            21,562             64,686          64,686
   Other operating expenses                                        24,154            13,069             50,953          37,629
                                                                  -------       -----------          ---------        --------

                                                                   45,716            34,631            115,639         102,315
                                                                  -------       -----------          ---------        --------

(LOSS) PROFIT BEFORE
  EXTRAORDINARY ITEM                                              (41,424)          346,181            (99,456)        296,895

EXTRAORDINARY ITEM - SHARE FROM
    LOCAL LIMITED PARTNERSHIP OF
    GAIN ON EXTINGUISHMENT OF DEBT                                    -             677,126                -           677,126
                                                                  -------        ----------          ---------        --------

NET (LOSS) PROFIT                                                $(41,424)       $1,023,307         $  (99,456)      $ 974,021
                                                                  =======         =========          =========        ========

(LOSS) PROFIT BEFORE EXTRAORDINARY
  ITEM ASSIGNABLE TO OTHER LIMITED PARTNERS                      $(40,594)       $  339,257         $  (97,466)      $ 290,957

EXTRAORDINARY ITEM - GAIN FROM LOCAL
  LIMITED PARTNERSHIP ON EXTINGUISHMENT
  OF DEBT ASSIGNABLE TO OTHER LIMITED PARTNERS                        -             663,584                -           663,584
                                                                  -------         ---------          ---------       ---------

NET (LOSS) PROFIT ASSIGNABLE TO OTHER
  LIMITED PARTNERS                                               $(40,594)       $1,002,841         $  (97,466)      $ 954,541
                                                                  =======         =========          =========        ========

(LOSS) PROFIT BEFORE EXTRAORDINARY
  ITEM PER OTHER LIMITED PARTNERSHIP INTEREST                    $     (4)       $       29         $       (8)      $      25

EXTRAORDINARY ITEM - GAIN FROM LOCAL
  LIMITED PARTNERSHIP ON EXTINGUISHMENT
  DEBT PER OTHER LIMITED PARTNERSHIP INTEREST                         -                  58                -                58
                                                                  -------         ---------          ---------        --------

 NET (LOSS) PROFIT PER OTHER LIMITED
  PARTNERSHIP INTEREST                                           $     (4)       $       87         $       (8)      $      83
                                                                  =======         =========          =========        ========
</TABLE>



                       See notes to financial statements.

                                      -2-
<PAGE>   4
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                    STATEMENT OF PARTNERS' EQUITY (DEFICIT)
                     NINE MONTHS ENDED SEPTEMBER 30, 1998
                                 (UNAUDITED)



<TABLE>
<CAPTION>
                                         The National         1133
                                           Housing         Fifteenth          Other
                                         Partnership      Street Three       Limited
                                            (NHP)          Associates        Partners          Total
                                         -----------       ----------        --------          -----
<S>                                      <C>               <C>              <C>              <C>
Deficit at January 1, 1998               $  (89,402)       $ (94,302)       $ 768,435        $ 584,731

Net loss -- nine months ended
  September 30, 1998                           (995)            (995)         (97,466)         (99,456)
                                          ---------         --------         --------         --------

Equity (deficit) at
  September 30, 1998                     $  (90,397)       $ (95,297)       $ 670,969        $ 485,275
                                          =========         =========        ========         ========

Percentage interest at
  September 30, 1998                              1%               1%              98%             100%
                                          =========         ========         ========         ========
                                                (A)              (B)              (C)
</TABLE>

(A)      General Partner
(B)      Original Limited Partner
(C)      Consists of 11,500 investment units





                       See notes to financial statements.

                                      -3-
<PAGE>   5
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                            STATEMENTS OF CASH FLOWS
                                  (UNAUDITED)


<TABLE>
<CAPTION>
                                                                                          Nine Months Ended September 30,
                                                                                        -----------------------------------
                                                                                             1998                    1997
                                                                                        ------------            -----------
<S>                                                                                      <C>                    <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Distributions from Local Limited Partnerships                                          $   13,908             $1,034,986
   Distributions received in excess of investment in
     Local Limited Partnerships                                                                  -                   15,698
   Payment of administrative and reporting fees to
     General Partner                                                                             -                 (619,985)
   Interest received                                                                          16,183                  9,342
   Operating expenses paid                                                                   (59,288)               (48,224)
                                                                                           ---------              ---------

   Net cash (used in) provided by operating activities                                       (29,197)               391,817

CASH FLOWS FROM INVESTING ACTIVITIES:
   Repayment of advances to Local Limited Partnerships                                           -                   16,310
                                                                                           ---------              ---------

NET (DECREASE) INCREASE IN CASH AND CASH
  EQUIVALENTS                                                                                (29,197)               408,127

CASH AND CASH EQUIVALENTS, BEGINNING OF
  PERIOD                                                                                     538,513                140,782
                                                                                           ---------              ---------

CASH AND CASH EQUIVALENTS, END OF PERIOD                                                  $  509,316             $  548,909
                                                                                           =========              =========

RECONCILIATION OF NET (LOSS) PROFIT TO NET CASH
  (USED IN) PROVIDED BY OPERATING ACTIVITIES:
  Net (loss) profit                                                                       $  (99,456)            $  974,021
                                                                                           ---------              ---------
  Adjustments to reconcile net (loss) profit to net cash
      (used in) provided by operating activities:
         Repayment of advances to Local Limited Partnerships                                     -                  (16,310)
         Distributions from Local Limited Partnerships                                        13,908              1,034,986
         Share of income from Local Limited Partnerships                                         -                 (357,860)
         Share of gain on extinguishment of debt                                                 -                 (677,126)
         Increase in prepaid expenses                                                            -                  (21,562)
              Increase (decrease) in administrative
                  and reporting fees payable                                                  64,686               (533,737)
         Decrease in accrued expenses                                                         (8,335)               (10,595)
                                                                                           ---------              ---------

         Total adjustments                                                                    70,259               (582,204)
                                                                                           ---------              ---------

   Net cash (used in) provided by operating activities                                    $  (29,197)            $  391,817
                                                                                           =========              =========
</TABLE>



                       See notes to financial statements.

                                      -4-
<PAGE>   6
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                         NOTES TO FINANCIAL STATEMENTS



(1)      ACCOUNTING POLICIES

         ORGANIZATION

         National Housing Partnership Realty Fund III (the "Partnership") is a
         limited partnership organized under the laws of the State of Maryland
         under the Maryland Revised Uniform Limited Partnership Act on May 10,
         1985. The Partnership was formed for the purpose of raising capital by
         offering and selling limited partnership interests and then investing
         in limited partnerships ("Local Limited Partnerships"), each of which
         owns and operates an existing rental housing project which is financed
         and/or operated with one or more forms of rental assistance or
         financial assistance from the U.S. Department of Housing and Urban
         Development ("HUD").

         The General Partner raised capital for the Partnership by offering and
         selling to additional limited partners 11,500 investment units. The
         Partnership acquired limited partnership interests ranging from 94.5%
         to 99% in twelve Local Limited Partnerships, which were organized to
         directly or indirectly own and operate existing rental housing
         projects.

         On June 3, 1997, Apartment Investment and Management Company, a
         Maryland corporation ("AIMCO" and, together with its subsidiaries and
         other controlled entities, the "AIMCO Group"), acquired all of the
         issued and outstanding capital stock of NHP Partners, Inc., a Delaware
         corporation ("NHP Partners"), and the AIMCO Group acquired all of the
         outstanding interests in NHP Partners Two Limited Partnership, a
         Delaware limited partnership ("NHP Partners Two"). The Acquisition was
         made pursuant to a Real Estate Acquisition Agreement, dated as of May
         22, 1997 (the "Agreement"), by and among AIMCO, AIMCO Properties,
         L.P., a Delaware limited partnership (the "Operating Partnership"),
         Demeter Holdings Corporation, a Massachusetts corporation ("Demeter"),
         Phemus Corporation, a Massachusetts corporation ("Phemus"), Capricorn
         Investors, L.P., a Delaware limited partnership ("Capricorn"), J.
         Roderick Heller, III and NHP Partners Two LLC, a Delaware limited
         liability company ("NHP Partners Two LLC"). NHP Partners owns all of
         the outstanding capital stock of the National Corporation for Housing
         Partnerships, a District of Columbia corporation ("NCHP"), which is
         the general partner of The National Housing Partnership, a District of
         Columbia limited partnership ("NHP"). Together, NCHP and NHP Partners
         Two own all of the outstanding partnership interests in NHP. NHP is
         the general partner of National Housing Partnership Realty Fund III (a
         Maryland Limited Partnership) (the "Registrant"). As a result of these
         transactions, the AIMCO Group has acquired control of the general
         partner of the Registrant and, therefore, may be deemed to have
         acquired control of the Registrant.

         The Original Limited Partner of the Partnership is 1133 Fifteenth
         Street Three Associates, whose limited partners were key employees of
         NCHP at the time the Partnership was formed and whose general partner
         is NHP.

         BASIS OF PRESENTATION

         The accompanying unaudited interim financial statements reflect all
         adjustments which are, in the opinion of management, necessary to a
         fair statement of the financial condition and results of operations
         for the interim periods presented. All such adjustments are of a
         normal and recurring nature.

         While the General Partner believes that the disclosures presented are
         adequate to make the information not misleading, it is suggested that
         these financial statements be read in conjunction with the financial
         statements and notes included in NHP Realty Fund III's Annual Report
         filed in Form 10-K for the year ended December 31, 1997.





                                      -5-
<PAGE>   7
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                         NOTES TO FINANCIAL STATEMENTS


(2)      INVESTMENTS IN AND ADVANCES TO LOCAL LIMITED PARTNERSHIPS

         The Partnership owns a 99% limited partnership interest in Brunswick
         Village Limited Partnership and 94.5% limited partnership interests
         (98% with respect to allocation of losses) in nine other Local Limited
         Partnerships. The Partnership also acquired a 99% limited partnership
         interest in Meadowood Townhouses I Limited Partnership which owns a
         99% limited partnership interest in an operating limited partnership
         which held title to two rental housing properties until their sale on
         July 15, 1997. The Partnership additionally acquired a 99% interest in
         Meadowood Townhouses III Limited Partnership which owns a 99% limited
         partnership interest in an operating limited partnership which holds
         title to one rental housing property. The Partnership's effective
         interest in these operating limited partnerships is 98.01%.

         Because the Partnership, as a limited partner, does not exercise
         control over the activities of the Local Limited Partnerships in
         accordance with the partnership agreements, these investments in Local
         Limited Partnerships are accounted for using the equity method. Thus,
         the investments (and the advances made to the Local Limited
         Partnerships as discussed below) are carried at cost plus the
         Partnership's share of the Local Limited Partnerships' profits less
         the Partnership's share of the Local Limited Partnerships' losses and
         distributions. However, because the Partnership is not legally liable
         for the obligations of the Local Limited Partnerships, and is not
         otherwise committed to provide additional support to them, it does not
         recognize losses once its investments, reduced for its share of losses
         and cash distributions, reach zero in each of the individual Local
         Limited Partnerships. As of December 31, 1996, investments in the
         twelve Local Limited Partnerships had been reduced to zero. During the
         nine months ended September 30, 1997, three properties owned by two
         Local Limited Partnerships were sold. As a result the Partnership
         recognized income of $357,860 from the gain on sale of Elden Terrace
         and an extraordinary gain of $677,126 on the extinguishment of debt
         related to the sale of Meadowoods I and II.  Both the gain on sale and
         the extraordinary gain were recorded after recognizing previously
         unrecognized losses of $568,164 and $2,347,585, respectively. As a
         result of these sales the Partnership's investment in these Local
         Limited Partnerships is $73,200 as of September 30, 1998. The
         Partnership did not recognize $691,089 and $806,272 of losses from the
         other ten Local Limited Partnerships during the nine months ended
         September 30, 1998 and 1997, respectively. As of September 30, 1998
         and December 31, 1997, the Partnership has not recognized a total of
         $14,440,929 and $13,749,840, respectively, of its allocated share of
         cumulative losses from the Local Limited Partnerships in which its
         investment is zero.

         Advances made by the Partnership to the individual Local Limited
         Partnerships are considered part of the Partnership's investment in
         Local Limited Partnerships. When advances are made, they are charged
         to operations as a loss on investment in the Local Limited Partnership
         using previously unrecognized cumulative losses. As discussed above,
         due to the cumulative losses incurred by the Local Limited
         Partnerships, the aggregate balance of investments in and advances to
         the remaining ten Local Limited Partnerships has been reduced to zero
         at September 30, 1998 and December 31, 1997. To the extent these
         advances are repaid by the Local Limited Partnerships in the future,
         the repayments will be credited as distribution and repayments
         received in excess of investment in Local Limited Partnerships. These
         advances are carried as a payable to the Partnership by the Local
         Limited Partnerships.

         No working capital advances occurred between the Partnership and the
         Local Limited Partnerships during the nine months ended September 30,
         1998 and 1997. Repayments of $16,310 and accrued interest of $5,178
         were made by two Local Limited Partnerships to the Partnership during
         the nine months ended September 30, 1997. No repayments were made
         during the nine months ended September 30, 1998. The combined amount
         carried as due to the Partnership by the Local Limited Partnerships
         was $522,159 as of September 30, 1998. Future advances made will be
         charged to operations; likewise, future repayments will be credited to
         operations.





                                      -6-
<PAGE>   8
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                         NOTES TO FINANCIAL STATEMENTS



         The following are combined statements of operations for the three and
         nine months ended September 30, 1998 and 1997, respectively, of the
         Local Limited Partnerships in which the Partnership has invested. The
         statements are compiled from financial statements of the Local Limited
         Partnerships, prepared on the accrual basis of accounting, as supplied
         by the management agents of the projects, and are unaudited.

                       COMBINED STATEMENTS OF OPERATIONS



<TABLE>
<CAPTION>
                                                        Three Months Ended                 Nine Months Ended
                                                           September 30,                      September 30,
                                               -------------------------------    ---------------------------------
                                                     1998              1997            1998                1997
                                               --------------    -------------    --------------       ------------
<S>                                             <C>              <C>               <C>                  <C>
Rental income                                    $ 1,533,220      $ 1,650,247       $ 4,593,927         $ 5,969,307
Other income                                          82,504          142,582           225,345             325,904
Gain on disposal of rental properties                    -            939,814               -               939,814
                                                  ----------       ----------        ----------          ----------

   Total income                                    1,615,724        2,732,643         4,819,272           7,235,025
                                                  ----------       ----------        ----------          ----------

Operating expenses                                 1,002,531        1,267,697         3,171,021           4,261,324
Interest, taxes and insurance                        541,321          587,916         1,640,209           2,080,509
Depreciation                                         237,264          270,746           711,679             961,202
                                                  ----------       ----------        ----------          ----------

   Total expenses                                  1,781,116        2,126,359         5,522,909           7,303,035
                                                  ----------       ----------        ----------          ----------

(Loss) profit before extraordinary item             (165,392)         606,284          (703,637)            (68,010)

Extraordinary Item - Gain on
   extinguishment of debt                                -          3,281,574               -             3,281,574
                                                  ----------       ----------        ----------          ----------

   Net (loss) profit                             $  (165,392)     $ 3,887,858       $  (703,637)        $ 3,213,564
                                                  ==========       ==========        ==========          ==========

National Housing Partnership Realty
   Fund III share of (losses) profits            $  (162,510)     $ 3,806,468       $  (691,089)        $ 3,144,464
                                                  ==========       ==========        ==========          ==========
</TABLE>


(3)      TRANSACTIONS WITH THE GENERAL PARTNER

         During the nine month periods ended September 30, 1998 and 1997, the
         Partnership accrued administrative and reporting fees payable to the
         General Partner in the amount of $64,686 for services provided to the
         Partnership. The Partnership has not made any payments to the General
         Partner for these fees during the nine months ended September 30.
         1998. The Partnership paid the General Partner $619,985 for these fees
         and accrued but unpaid fees from prior years during the nine months
         ended September 30, 1997. The amount due the General Partner by the
         Partnership for administrative and reporting fees was $64,686 at
         September 30, 1998, while there were no fees due at December 31, 1997.





                                      -7-
<PAGE>   9
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
                         NOTES TO FINANCIAL STATEMENTS



         Accrued administrative and reporting fees payable to the General
         Partner are paid as cash flow permits or from proceeds generated from
         the sale or refinancing of one or more of the underlying properties of
         the Local Limited Partnerships.


(4)      DISPOSAL OF RENTAL PROPERTIES

         On May 2, 1996, Meadowood Townhouses I Local Limited Partnership
         entered into an Agreement of Sale with Community Preservation and
         Development Corporation, to sell its two properties, Meadowood
         Townhouses I and II pursuant to the terms of Low Income Housing
         Preservation and Resident Homeownership Act of 1990 ("LIHPRHA"). The
         purchase price was based on the properties' Transfer Preservation
         Value, as approved by the United States Department of Housing and
         Urban Development ("HUD"). During the six months ended June 30, 1997,
         funding was approved for the sale of Meadowood Townhouses I and II,
         and final settlement occurred on July 15, 1997. Total LIHPRHA grant
         money received for the properties was $3,336,388, comprised of
         $1,558,253 for Meadowoods Townhouses I and $1,778,135 for Meadowood
         Townhouses II. The holders of the deferred acquisition notes were
         repaid from a portion of the LIHPRHA grant money at an agreed upon
         discounted amount. The mortgage notes were assumed by the purchaser.
         During the quarter ended September 30, 1997 the Partnership received
         net proceeds from the sale of $677,126. The Partnership's share of the
         gain from this transaction has been recorded in the accompanying
         statements of operations for the three and nine months ended September
         30, 1997 as an extraordinary item - gain on extinguishment of debt.

         In addition, during the six months ended June 30, 1997, Elden Limited
         Partnership entered into an Agreement of Sale with Southport Financial
         Services, Inc., to sell its property, Elden Terrace Apartments. The
         purchase price for the sale was $2,241,667, which is $375,000 above
         the mortgage note of $1,866,667. Southport Financial Services, Inc.
         also assumed the deferred acquisition note and accrued interest
         totaling $3,505,225 due to the note holders. Final settlement occurred
         on July 31, 1997. During the quarter ended September 30, 1997 the
         Partnership received net proceeds from the sale of $357,860.  The
         Partnership's share of the gain from this transaction has been
         recorded in the accompanying statements of operations for the three
         and nine months ended September 30, 1997 as the Partnership's share of
         income from Local Limited Partnership.





                                      -8-
<PAGE>   10



ITEM 2 -     MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
             AND RESULTS OF OPERATIONS

                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)


The Private Securities Litigation Reform Act of 1995 provides a "safe harbor"
for forward-looking statements in certain circumstances. Certain information
included in this Report and other Partnership filings (collectively "SEC
Filings") under the Securities Act of 1933, as amended, and the Securities
Exchange Act of 1934, as amended (as well as information communicated orally or
in writing between the dates of such SEC Filings) contains or may contain
information that is forward-looking, including statements regarding the effect
of government regulations. Actual results may differ materially from those
described in the forward-looking statements and will be affected by a variety
of factors including national and local economic conditions, the general level
of interest rates, terms of governmental regulations that affect the
Partnership and interpretations of those regulations, the competitive
environment in which the properties owned by the Local Limited Partnerships
operate, the availability of working capital and dispositions of properties
owned by the Partnership.

YEAR 2000 COMPLIANCE

General Description of the Year 2000 Issue and the Nature and Effects of the
Year 2000 on Information Technology (IT) and Non-IT Systems

The Year 2000 Issue is the result of computer programs being written using two
digits rather than four to define the applicable year.  The Partnership is
dependent upon the General Partner and its affiliates for management and
administrative services ("Managing Agent").  Any computer programs or hardware
that have date-sensitive software or embedded chips may recognize a date using
"00" as the year 1900 rather than the year 2000.  This could result in a system
failure or miscalculations causing disruptions of operations, including, among
other things, a temporary inability to process transactions, send invoices, or
engage in similar normal business activities.

The Managing Agent has determined that it will be required to modify or replace
significant portions of its software and certain hardware so that those systems
will properly utilize dates beyond December 31, 1999. The Managing Agent
presently believes that with modifications or replacements of existing software
and certain hardware, the Year 2000 Issue can be mitigated. However, if such
modifications and replacements are not made, or are not completed timely, the
Year 2000 Issue could have a material impact on the operations of the Managing
Agent and the Partnership.

Status of Progress in Becoming Year 2000 Compliant

The Managing Agent's plan to resolve the Year 2000 Issue involves the following
four phases: assessment, remediation, testing and implementation.  To date, the
Managing Agent has fully completed its assessment of all information systems
that could be significantly affected by the Year 2000, and has begun the
remediation, testing and implementation phase on both hardware and software
systems.  Assessments are continuing in regards to embedded systems in
operating equipment.  The Managing Agent anticipates having all phases complete
by June 1, 1999.

In addition to the areas the Partnership is relying on the Managing Agent to
verify compliance with,  the Partnership has certain operating equipment,
primarily at the property sites,  which needed to be evaluated for Year 2000
compliance.  The focus of the General Partner was to the security systems,
elevators, heating-ventilation-air-conditioning systems, telephone systems and
switches, and sprinkler systems. The General Partner is currently engaged in
the identification of all non-compliant operational systems, and is in the
process of estimating the costs associated with any potential modifications or
replacements needed to such systems in order for them to be Year 2000
compliant.  It is not expected that such costs would have a material adverse
affect upon the operations of the Partnership.





                                      -9-
<PAGE>   11
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
          MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                           AND RESULTS OF OPERATIONS


Risk Associated with the Year 2000

The General Partner believes that the Managing Agent has an effective program
in place to resolve the Year 2000 issue in a timely manner and has appropriate
contingency plans in place for critical applications that could affect the
Partnership's operations.   To date, General Partner is not aware of any
external agent with a Year 2000 issue that would materially impact the
Partnership's results of operations, liquidity or capital resources.  However,
the General Partner has no means of ensuring that external agents will be Year
2000 compliant.  The  General Partner does not believe that the inability of
external agents to complete their Year 2000 resolution process in a timely
manner will have a material impact on the financial position or results of
operations of the Partnership.  However, the effect of non-compliance by
external agents is not readily determinable.


LIQUIDITY AND CAPITAL RESOURCES

The properties in which the Partnership has invested, through its investments
in the Local Limited Partnerships, receive one or more forms of assistance from
Federal, state or local governments or agencies. As a result, the Local Limited
Partnerships' ability to transfer funds either to the Partnership or among
themselves in the form of cash distributions, loans or advances is generally
restricted by these government-assistance programs. These restrictions,
however, are not expected to impact the Partnership's ability to meet its cash
obligations.

For the past several years, various proposals have been advanced by HUD,
Congress and others proposing the restructuring of HUD's rental assistance
programs under Section 8 of the United States Housing Act of 1937 ("Section
8"), under which 503 units, 41 percent of the total units owned by the
properties in which the Partnership has invested, receive rental subsidies.
These subsidies are generally provided pursuant to project-based Housing
Assistance Payment Contracts ("HAP Contracts") between HUD and the owners of
the properties. On October 27, 1997, the President signed into law the
Multifamily Assisted Housing Reform and Affordability Act of 1997 (the "1997
Housing Act"). Under the 1997 Housing Act, the mortgage financing and HAP
contracts of certain properties assisted under Section 8, with rents above
market levels and financed with HUD-insured mortgage loans, will be
restructured by adjusting subsidized rents to market levels, thereby reducing
subsidy levels, and lowering required debt service costs as needed to ensure
financial viability at the reduced rents and subsidy levels. The 1997 Housing
Act retains project-based subsidies for most properties (properties in rental
markets with limited supply, properties serving the elderly, and certain other
properties).

The 1997 Housing Act phases out project-based subsidies on selected properties
servicing families not located in rental markets with limited supply,
converting such subsidies to a tenant-based subsidy. Under a tenant-based
system, rent vouchers would be issued to qualified tenants who then could elect
to reside at properties of their choice, provided the tenant has the financial
ability to pay the difference between the selected property's monthly rent and
the value of the voucher, which would be established based on HUD's regulated
fair market rent for the relevant geographical areas. The 1997 Housing Act
provides that properties will begin the restructuring process in federal fiscal
year 1999 (beginning October 1, 1998), and that HUD will issue final
regulations implementing 1997 Housing Act on or before October 27, 1998.
Congress has elected to renew HAP Contracts expiring before October 1, 1998 for
one year terms, generally at existing rents, so long as the properties remain
in compliance with the HAP Contracts. While the Partnership does not expect the
provisions of the 1997 Housing Act to result in a significant number of tenants
relocating from properties owned by the Local Limited Partnerships, there can
be no assurance that the provisions will not significantly affect the
operations of the properties of the Local Limited Partnerships. Furthermore,
there can be no assurance that other changes in Federal housing subsidy policy
will not occur. Any such changes could have an adverse effect on the operation
of the Partnership.





                                      -10-
<PAGE>   12
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
          MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                           AND RESULTS OF OPERATIONS



Net cash used in operations for the nine months ended September 30, 1998 was
$29,197 as compared to net cash provided by operations of $391,817 for the nine
months ended September 30, 1997. The change from cash provided by operations to
cash used in operations resulted primarily from a decrease in distributions
from Local Limited Partnerships of $1,021,078 resulting from the sales of three
properties, partially offset by a decrease in the payment of administrative and
reporting fees to the General Partner of $619,985 during the nine months ended
September 30, 1998, compared to the nine months ended September 30, 1997.

No working capital advances occurred between the Partnership and the Local
Limited Partnerships during the nine months ended September 30, 1998 and 1997.
Repayments of $16,310 and accrued interest of $5,178 were made by two Local
Limited Partnerships to the Partnership during the nine months ended September
30, 1997. No repayments were made during the nine months ended September 30,
1998. The combined amount carried as due to the Partnership by the Local
Limited Partnerships was $522,159 as of September 30, 1998.  Future advances
made will be charged to operations; likewise, future repayments will be
credited to operations.

Distributions received from Local Limited Partnerships represent the
Partnership's proportionate share of the excess cash available for distribution
from the Local Limited Partnerships. As a result of the use of the equity
method of accounting for the Partnership's investments, as of September 30,
1998, investments in ten Local Limited Partnerships had been reduced to zero.
For these investments, cash distributions received are recorded in income as
distributions received in excess of investment in Local Limited Partnerships.
For those investments not reduced to zero, distributions received are recorded
as distributions from Local Limited Partnerships. During the nine months ended
September 30, 1997, cash distributions of $15,698 were received from two Local
Limited Partnerships. In addition, during the nine months ended September 30,
1998 and 1997, the Partnership received $13,908 and $1,034,986, respectively,
in distributions from two Local Limited Partnerships resulting from proceeds
from the disposal of their rental properties. The receipt of distributions in
the future is dependent upon the operations of the underlying properties of the
Local Limited Partnerships to generate sufficient cash for distribution in
accordance with applicable HUD regulations.

Cash and cash equivalents of $509,316 on hand at September 30, 1998, plus any
distributions from the underlying operations of the combined Local Limited
Partnerships, is expected to adequately fund the operations of the Partnership
in the current year. However, there can be no assurance that future
distributions will be adequate to fund the operations beyond the current year.

All of the Local Limited Partnerships in which the Partnership has invested
carry deferred acquisition notes. The deferred acquisition notes related to
Meadowood Townhouses III Limited Partnership as discussed below reached final
maturity in January 1998.  The deferred acquisition note related to Brunswick
Village Limited Partnership will reach final maturity in February 1999. The
notes related to the other eight Local Limited Partnerships will reach final
maturity during December 1999. All notes are secured by both the Partnership's
and the General Partner's interests in the Local Limited Partnerships. In the
event of a default on the notes, the note holders would be able to assume the
General Partner's and the Partnership's interests in the Local Limited
Partnerships. Should the Partnership lose its interest in a Local Limited
Partnership, partners in the Partnership may incur adverse tax consequences.
The impact of the tax consequence is dependent upon each partner's individual
tax situation. There can be no assurance that the General Partner will be
successful in extending or restructuring the deferred acquisition notes as they
mature.

On May 2, 1996, the Meadowood Townhouses III Limited Partnership entered into
Agreement of Sale with Community Preservation and Development Corporation,
pursuant to the terms of the Low Income Housing





                                      -11-
<PAGE>   13
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
          MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                           AND RESULTS OF OPERATIONS



Preservation and Resident Homeownership Act of 1990 ("LIHPRHA"). The purchase
price was to be based on the project's Transfer Preservation Value, as approved
by HUD. Settlement was pending Congressional appropriation of LIHPRHA funds to
HUD. This appropriation did not transpire and therefore this sale opportunity
expired. In connection with the expired sale opportunity, a Forebearance
Agreement was executed, which extended the maturity date of the deferred
acquisition note in the amount of $4,995,980 including accrued interest at
December 31, 1997, made by the Meadowood Townhouses III Limited Partnership.
Under the terms of this agreement, the initial period of forebearance expired
on April 30, 1997. Such funding was not approved by April 30, 1997 and a
further extension of forebearance until January 2, 1998 was granted to permit
the General Partner to submit an alternative plan to the note holders, and to
negotiate and close such plan. The General Partner is currently attempting to
negotiate an extension of the due date of the deferred acquisition note. If
such an extension is not negotiated, the Partnership shall cause title to the
Partnership's interest in the Local Limited Partnership to be conveyed to the
note holders. There can be no assurance that the efforts will be successful.


RESULTS OF OPERATIONS

The Partnership has invested as a limited partner in twelve Local Limited
Partnerships which operate ten rental housing properties.  In prior years,
results of operations of NHP Realty Fund III were significantly impacted by the
Partnership's share of the losses of the Local Limited Partnerships. These
losses included depreciation and accrued deferred acquisition note interest
expense which are non-cash in nature. Because the investments in and advances
to Local Limited Partnerships have been reduced to zero, the Partnership's
share of the operations of the Local Limited Partnerships is no longer being
recorded. During the nine months ended September 30, 1997, three properties
owned by two Local Limited Partnerships were sold. As a result the Partnership
recognized income of $357,860 from the gain on sale of Elden Terrace and an
extraordinary gain of $677,126 on the extinguishment of debt related to the
sale of Meadowoods I and II. Both the gain on sale and the extraordinary gain
were recorded after recognizing previously unrecognized losses of $568,164 and
$2,347,585, respectively. The Partnership did not recognize $691,089 and
$806,272 of losses from the other ten Local Limited Partnerships during the
nine months ended September 30, 1998 and 1997. As of September 30, 1998 and
December 31, 1997, the Partnership has not recognized a total of $14,440,929
and $13,749,840, respectively, of its allocated share of cumulative losses from
the Local Limited Partnerships in which its investment is zero.

The Partnership's had a net loss of  $99,456 for the nine months ended
September 30, 1998 compared to a net profit of $974,021 for the nine months
ended September 30, 1997. Net loss per unit of other limited partnership
interest was $8 for the nine months ended September 30, 1998 compared to a net
profit per unit of $83 for the nine months ended September 30, 1997 for the
11,500 units outstanding throughout both periods. The change from a net profit
to a loss was primarily due to the Partnership recognizing its share of income
from Local Limited Partnerships of $357,860 resulting from the sale of Elden
Terrace and a gain on extinguishment of debt of $677,126 resulting from the
sale of Meadowoods I and II during the nine months ended September 30, 1997.
There were no such gains recognized during the nine months ended September 30,
1998. During the nine months ended September 30, 1998, the Partnership incurred
operating expenses of approximately $51,900 related to complying with SEC
filing, auditing, and reporting and mailing requirements. The Partnership did
not recognize $691,089 of its allocated share of losses from the ten Local
Limited Partnerships for the nine months ended September 30, 1998, as the
Partnership's net carrying basis in these Partnerships had been previously
reduced to zero. The Partnership's share of losses before extraordinary item
from the Local Limited Partnerships, if not limited to its investment account
balance, would have increased $586,795 between periods, primarily due to the
gain on sale of Elden Terrace recorded during 1997.





                                      -12-
<PAGE>   14
                  NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                        (A MARYLAND LIMITED PARTNERSHIP)
          MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                           AND RESULTS OF OPERATIONS



The Partnership's had a net loss of  $41,424 for the three months ended
September 30, 1998 compared to a net profit of $1,023,307 for the three months
ended September 30, 1997. Net loss per unit of other limited partnership
interest was $4 for the three months ended September 30, 1998 compared to a net
profit per unit of $87 for the three months ended September 30, 1997 for the
11,500 units outstanding throughout both periods. The change from a net profit
to a loss was primarily due to the Partnership recognizing its share of income
from Local Limited Partnerships of $357,860 resulting from the sale of Elden
Terrace and a gain on extinguishment of debt of $677,126 resulting from the
sale of Meadowoods I and II during the three months ended September 30, 1997.
There were no such gains recognized during the three months ended September 30,
1998. During the three months ended September 30, 1998, the Partnership
incurred operating expenses of approximately $15,700 related to complying with
SEC filing, auditing, and reporting and mailing requirements. The Partnership
did not recognize $162,510 of its allocated share of losses from the ten Local
Limited Partnerships for the three months ended September 30, 1998, as the
Partnership's net carrying basis in these Partnerships had been previously
reduced to zero. The Partnership's share of losses before extraordinary item
from the Local Limited Partnerships, if not limited to its investment account
balance, would have increased $720,220 between periods, primarily due to the
gain on sale of Elden Terrace recorded during 1997.

PART II - OTHER INFORMATION

ITEM 6  -  EXHIBITS AND REPORTS ON FORM 8-K

         (a)     Exhibits

                 Exhibit No.

                 27       Financial Data Schedule





                                      -13-
<PAGE>   15



                                   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.



                            NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                            --------------------------------------------
                            (Registrant)


                            By:     The National Housing Partnership,
                                    its sole General Partner


                            By:     National Corporation for Housing
                                    Partnerships, its sole General Partner



November 13, 1998           By:                         /s/
-----------------                   ---------------------------------------
                                    Troy D. Butts
                                    As Senior Vice President and Chief Financial
                                    Officer





                                      -14-