<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 JUNE 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>
                                                                             June 30,
                                                                               1998         December 31,
                                                                            (Unaudited)         1997
                                                                           ------------     ------------

                                    ASSETS
                                    ------

<S>                                                                         <C>              <C>
Cash and cash equivalents                                                   $ 506,015        $ 538,513
Investments in and advances to Local Limited Partnerships (Note 2)             87,108           87,108
                                                                            ---------        ---------

                                                                            $ 593,123        $ 625,621
                                                                            =========        =========

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

Liabilities:
   Administrative and reporting fee payable to General Partner (Note 3)     $  43,124         $      -
   Accrued expenses                                                            23,300           40,890
                                                                            ---------        ---------

                                                                               66,424           40,890
                                                                            ---------        ---------

Partners' equity (deficit):
   General Partner -- The National Housing Partnership (NHP)                  (89,982)         (89,402)
   Original Limited Partner -- 1133 Fifteenth Street Three Associates         (94,882)         (94,302)
   Other Limited Partners -- 11,500 investment units                          711,563          768,435
                                                                            ---------        ---------

                                                                              526,699          584,731
                                                                            ---------        ---------

                                                                            $ 593,123        $ 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               Six Months Ended
                                                          June 30,                        June 30,
                                                  ------------------------        ------------------------
                                                    1998           1997             1998            1997
                                                  --------        --------        --------        --------
<S>                                              <C>              <C>            <C>              <C>
REVENUES:
   Distributions and repayments received in
    excess of investment in and advances to
    Local Limited Partnerships (Note 2)          $       -        $ 15,698       $       -        $ 15,698
   Interest income                                   5,608           1,428          11,891           2,700
                                                  --------        --------        --------        --------

                                                     5,608          17,126          11,891          18,398
                                                  --------        --------        --------        --------

COSTS AND EXPENSES:
   Administrative and reporting fees to
    General Partner (Note 3)                        21,562          21,562          43,124          43,124
   Other operating expenses                         12,425          11,221          26,799          24,560
                                                  --------        --------        --------        --------


                                                    33,987          32,783          69,923          67,684
                                                  --------        --------        --------        --------

NET LOSS                                          $(28,379)       $(15,657)       $(58,032)       $(49,286)
                                                  ========        ========        ========        ========

NET LOSS ASSIGNABLE TO
  LIMITED PARTNERS                                $(27,813)       $(15,343)       $(56,872)       $(48,300)
                                                  ========        ========        ========        ========

NET LOSS PER LIMITED
  PARTNERSHIP INTEREST                            $     (2)       $     (1)       $     (5)       $     (4)
                                                  ========        ========        ========        ========
</TABLE>




                      See notes to financial statements.

                                    -2-


<PAGE>   4



                 NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                       (A MARYLAND LIMITED PARTNERSHIP)
                   STATEMENT OF PARTNER'S EQUITY (DEFICIT)
                                 (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 -- six months ended                         
  June 30, 1998                                                       (580)               (580)         (56,872)         (58,032)
                                                              ------------        ------------        ---------        ---------
                                                     
Equity (deficit) at June 30, 1998                             $    (89,982)       $    (94,882)       $ 711,563        $ 526,699
                                                              ============        ============        =========        =========
                                                     
Percentage interest at June 30, 1998                                     1%                  1%              98%             100%
                                                              ============        ============        =========        =========
                                                                       (A)                 (B)              (C)
</TABLE>                                             
                                                     
(A) General Partner                                  
(B) Original Limited Partner
(C) Consists of 11,500 investment units of 0.008522% held by 927 investors


                      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>
                                                                 Six Months Ended June 30,
                                                              -----------------------------
                                                                  1998             1997
                                                              -----------        ----------
<S>                                                           <C>               <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Distributions received in excess of investment in
      Local Limited Partnerships                              $        -        $  15,698
   Interest received                                              11,891            2,700
   Operating expenses paid                                       (44,389)         (44,155)
                                                               ---------        ---------

   Net cash used in operating activities                         (32,498)         (25,757)

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

CASH AND CASH EQUIVALENTS, END OF PERIOD                       $ 506,015        $ 115,025
                                                               =========        =========

RECONCILIATION OF NET LOSS TO NET CASH
  USED IN OPERATING ACTIVITIES:
   Net loss                                                    $ (58,032)       $ (49,286)
                                                               ---------        ---------
   Adjustments to reconcile net loss to net cash used in
     operating activities:
      Increase in administrative and reporting
        fees payable                                              43,124           43,124
      Decrease in accrued expenses                               (17,590)         (19,595)
                                                               ---------        ---------

      Total adjustments                                           25,534           23,529
                                                               ---------        ---------

   Net cash used in operating activities                       $ (32,498)       $ (25,757)
                                                               =========        =========
</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 at a price
      of $1,000 per unit. 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. As a result, the Partnership did not recognize $662,004 of losses
      from these twelve Local Limited Partnerships during the six months ended
      June 30, 1997. During the year ended December 31, 1997, three properties
      owned by two Local Limited Partnerships were sold, and as a result the
      Partnership's investment in these Local Limited Partnerships is $87,108.
      The Partnership did not recognize $528,579 of losses from the remaining
      ten Local Limited Partnerships during the six months ended June 30, 1998.
      As of June 30, 1998 and December 31, 1997, the Partnership has not
      recognized a total of $14,278,419 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 June 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 or repayments occurred between the Partnership
      and the Local Limited Partnerships during the six months ended June 30,
      1998 and 1997. The combined amount carried as due to the Partnership by
      the Local Limited Partnerships was $522,159 as of June 30, 1998. Future
      advances made will be charged to operations; likewise, future repayments
      will be credited to operations.


      The following are combined statements of operations for the three and six
      months ended June 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.


                                    -6-

<PAGE>   8


                 NATIONAL HOUSING PARTNERSHIP REALTY FUND III
                       (A MARYLAND LIMITED PARTNERSHIP)
                        NOTES TO FINANCIAL STATEMENTS


                      COMBINED STATEMENTS OF OPERATIONS



<TABLE>
<CAPTION>
                                                                  Three Months Ended                       Six Months Ended
                                                                       June 30,                                June 30,
                                                            ------------------------------        ------------------------------
                                                                1998               1997               1998               1997
                                                            ------------       -----------        -----------        -----------
<S>                                                         <C>                <C>                <C>                <C>        
Rental income                                               $ 1,489,486        $ 2,153,127        $ 3,060,707        $ 4,319,060
Other income                                                     64,997             98,334            142,841            183,322
                                                            -----------        -----------        -----------        -----------
                                                     
   Total income                                               1,554,483          2,251,461          3,203,548          4,502,382
                                                            -----------        -----------        -----------        -----------
                                                     
Operating expenses                                            1,123,151          1,544,577          2,168,490          2,993,627
Interest, taxes and insurance                                   533,356            715,864          1,098,888          1,492,593
Depreciation                                                    235,524            343,987            474,415            690,456
                                                            -----------        -----------        -----------        -----------
                                                     
   Total expenses                                             1,892,031          2,604,428          3,741,793          5,176,676
                                                            -----------        -----------        -----------        -----------
                                                     
Net loss                                                    $  (337,548)       $  (352,967)       $  (538,245)       $  (674,294)
                                                            ===========        ===========        ===========        ===========
                                                     
National Housing Partnership                         
 Realty Fund III share of losses                            $  (331,615)       $  (346,794)       $  (528,579)       $  (662,004)
                                                            ===========        ===========        ===========        ===========
</TABLE>                                             


(3)   TRANSACTIONS WITH THE GENERAL PARTNER

      During the six month periods ended June 30, 1998 and 1997, the Partnership
      accrued administrative and reporting fees payable to the General Partner
      in the amount of $43,124 for services provided to the Partnership. The
      Partnership has not made any payments to the General Partner for these
      fees during the respective periods. The amount due the General Partner by
      the Partnership for administrative and reporting fees was $43,124 at June
      30, 1998, while there were no fees due at December 31, 1997.

      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.





                                    -7-


<PAGE>   9



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.

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. 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,
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 potentially reducing rent subsidies,
and lowering required debt service costs as needed to ensure financial viability
at the reduced rents and rent subsidies. 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 such tenants have the financial ability to
pay the difference between the selected properties' monthly rent and the value
of the vouchers, 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. With respect to
Housing Assistance Payments Contracts ("HAP Contracts") expiring before October
1, 1998, Congress has elected to renew them 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 operations of the
Partnership.



                                      -8-
<PAGE>   10

                 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 six months ended June 30, 1998 was $32,498
as compared to net cash used in operations of $25,757 for the six months ended
June 30, 1997. The increase in net cash used in operations resulted primarily
from a decrease in distributions received in excess of investment in Local
Limited Partnerships, partially offset by an increase in interest income
received during the six months ended June 30, 1998, compared to the six months
ended June 30, 1997.

No working capital advances or repayments occurred between the Partnership and
the Local Limited Partnerships during the six months ended June 30, 1998 and
1997. The combined amount carried as due to the Partnership by the Local Limited
Partnerships was $522,159 as of June 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 June 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. There were no cash
distributions during the six months ended June 30, 1998, while cash
distributions of $15,698 were received from two Local Limited Partnerships
during the six months ended June 30, 1997. 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 $506,015 on hand at June 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 due the original owner of each Property. 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 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 



                                      -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


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.

The Partnership's had a net loss of $58,032 for the six months ended June 30,
1998 compared to a net loss of $49,286 for the six months ended June 30, 1997.
Net loss per unit of limited partnership interest increased from $4 to $5 for
the 11,500 units outstanding throughout both periods. The increase in net loss
was primarily due to a decrease in distributions received in excess of
investment in and advances to Local Limited Partnerships, partially offset by an
increase in interest income. The Partnership did not recognize $528,579 of its
allocated share of losses from the ten Local Limited Partnerships for the six
months ended June 30, 1998, as the Partnership's net carrying basis in these
Partnerships had been previously reduced to zero. The Partnership's share of
losses from the Local Limited Partnerships, if not limited to its investment
account balance, would have decreased $133,425 between periods, primarily due to
the decrease in number of rental properties owned by the Partnership during the
six months ended June 30, 1998 compared to the six months ended June 30, 1997 as
a result of the sales of three rental properties during the third quarter of
1997.

PART II - OTHER INFORMATION

ITEM 6  - EXHIBITS AND REPORTS ON FORM 8-K

      (a)   Exhibits

            Exhibit No.
            -----------

            27    Financial Data Schedule






                                    -10-


<PAGE>   12




                                  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.



<TABLE>
<S>                     <C>
                        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



August 14, 1998         By:                          /s/
---------------               ----------------------------------------------------
                              Troy D. Butts
                              As Senior Vice President and Chief Financial Officer
                                                                                  
                                                                                  
</TABLE>

                                      -11-