<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 MARCH 31, 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>
                                                                                March 31,
                                                                                  1998          December 31,
                                                                               (Unaudited)         1997
                                                                              ------------      ------------ 
<S>                                                                           <C>               <C>      
                                     ASSETS
Cash and cash equivalents                                                      $ 544,172        $ 538,513
Investments in and advances to Local Limited Partnerships (Note 2)                87,108           87,108
                                                                               ---------        ---------

                                                                               $ 631,280        $ 625,621
                                                                               =========        =========

                   LIABILITIES AND PARTNERS' EQUITY (DEFICIT)

Liabilities:
    Administrative and reporting fee payable to General Partner (Note 3)       $  21,562        $    --
    Accrued expenses                                                              54,640           40,890
                                                                               ---------        ---------

                                                                                  76,202           40,890
                                                                               ---------        ---------

Partners' equity (deficit):
    General Partner -- The National Housing Partnership (NHP)                    (89,699)         (89,402)
    Original Limited Partner -- 1133 Fifteenth Street Three Associates .         (94,599)         (94,302)
    Other Limited Partners -- 11,500 investment units                            739,376          768,435
                                                                               ---------        ---------

                                                                                 555,078          584,731
                                                                               ---------        ---------

                                                                               $ 631,280        $ 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 March 31,
                                               ----------------------------
                                                 1998            1997
                                                 ----            ----
<S>                                            <C>             <C>     
REVENUES:

    Interest income                            $  6,283        $  1,272
                                               --------        --------


COSTS AND EXPENSES:

    Administrative and reporting fees to
      General Partner (Note 3)                   21,562          21,562
    Other operating expenses                     14,374          13,339
                                               --------        --------

                                                 35,936          34,901
                                               --------        --------

NET LOSS                                       $(29,653)       $(33,629)
                                               ========        ========

NET LOSS ASSIGNABLE TO
  LIMITED PARTNERS                             $(29,059)       $(32,957)
                                               ========        ========

NET LOSS PER LIMITED
  PARTNERSHIP INTEREST                         $     (3)       $     (3)
                                               ========        ========
</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 -- three months ended
  March 31, 1998                                (297)             (297)          (29,059)          (29,653)
                                           ---------         ---------         ---------         ---------

Equity (deficit) at March 31, 1998         $ (89,699)        $ (94,599)        $ 739,376         $ 555,078
                                           =========         =========         =========         =========

Percentage interest at March 31, 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 921 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>
                                                                   Three Months Ended March 31,
                                                                   ----------------------------
                                                                      1998            1997
                                                                   ----------       ---------
<S>                                                                <C>              <C>      
CASH FLOWS FROM OPERATING ACTIVITIES:
    Interest received                                              $   6,283        $   1,272
    Operating expenses paid                                             (624)          (1,339)
                                                                   ---------        ---------

    Net cash provided by (used in) operating activities                5,659              (67)

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

CASH AND CASH EQUIVALENTS, END OF PERIOD                           $ 544,172        $ 140,715
                                                                   =========        =========

RECONCILIATION OF NET LOSS TO NET CASH
   PROVIDED BY (USED IN) OPERATING ACTIVITIES:
     Net loss                                                      $ (29,653)       $ (33,629)
                                                                   ---------        ---------
     Adjustments to reconcile net loss to net cash (used in)
       provided by operating activities:
         Increase in administrative and reporting
                  fees payable                                        21,562           21,562
         Increase in accrued expenses                                 13,750           12,000
                                                                   ---------        ---------

         Total adjustments                                            35,312           33,562
                                                                   ---------        ---------

    Net cash provided by (used in) operating activities            $   5,659        $     (67)
                                                                   =========        =========
</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 $315,210 of losses from these
         twelve Local Limited Partnerships during the three months ended March
         31, 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 $196,964 of losses from the
         remaining ten Local Limited Partnerships during the three months ended
         March 31, 1998. As of March 31, 1998 and December 31, 1997, the
         Partnership has not recognized a total of $13,946,804 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 March 31, 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 three months
         ended March 31, 1998 and 1997. The combined amount carried as due to
         the Partnership by the Local Limited Partnerships was $522,159 as of
         March 31, 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
         months ended March 31, 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 March 31,
                                                   ------------------------------
                                                       1998               1997
                                                   -----------        -----------
<S>                                                <C>                <C>        
Rental income                                      $ 1,571,221        $ 2,165,933
Other income                                            77,844             84,988
                                                   -----------        -----------

    Total income                                     1,649,065          2,250,921
                                                   -----------        -----------

Operating expenses                                   1,045,339          1,449,050
Interest, taxes and insurance                          565,532            776,729
Depreciation                                           238,891            346,469
                                                   -----------        -----------

    Total expenses                                   1,849,762          2,572,248
                                                   -----------        -----------

Net loss                                           $  (200,697)       $  (321,327)
                                                   ===========        ===========

National Housing Partnership Realty Fund III
   share of losses                                 $  (196,964)       $  (315,210)
                                                   ===========        ===========
</TABLE>


(3)      TRANSACTIONS WITH THE GENERAL PARTNER

         During the three month periods ended March 31, 1998 and 1997, the
         Partnership accrued administrative and reporting fees payable to the
         General Partner in the amount of $21,562 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 $21,562 at March 31, 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 provided by operations for the three months ended March 3 1998 was
$5,659 as compared to net cash used in operations of $67 for the three months
ended March 31, 1997. The increase in net cash provided by operations resulted
primarily from an increase in interest income received and a decrease in
operating expenses paid during the three months ended March 31, 1998, compared
to the three months ended March 31, 1997.

No working capital advances or repayments occurred between the Partnership and
the Local Limited Partnerships during the three months ended March 31, 1998 and
1997. The combined amount carried as due to the Partnership by the Local Limited
Partnerships was $522,159 as of March 31, 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 December 31, 1997,
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 three months ended March 31, 1998 and 1997,
respectively. 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 $544,172 on hand at March 31, 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. All other
notes will reach final maturity during 1999. These 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. 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 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 

                                      -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


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 $29,653 for the three months ended March 31,
1998 compared to a net loss of $33,629 for the three months ended March 31,
1997. Net loss per unit of limited partnership interest was $3 for the 11,500
units outstanding throughout both periods. The decrease in net loss was
primarily due to an increase in interest income. The Partnership did not
recognize $196,964 of its allocated share of losses from the ten Local Limited
Partnerships for the three months ended March 31, 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 $118,246 between
periods, primarily due to the decrease in number of rental properties owned by
the Partnership in the three months ended March 31, 1998 compared to the three
months ended March 31, 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


                                      -12-
<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.



                     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



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


                                      -13-