<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

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

                                    FORM 10-Q

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

(Mark One)

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


          For the quarterly period ended June 30, 1998 . . . . . . . . . . . .

                                                      OR

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

          For the transition period from ________________ to _________________

                               COMMISSION FILE NO.
                                     0-14105

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

                        MURRAY INCOME PROPERTIES I, LTD.
             (Exact Name of Registrant as Specified in its Charter)


               TEXAS                                      75-1946214
     (State or Other Jurisdiction of                   (I.R.S. Employer
     Incorporation or Organization)                    Identification No.)

   5550 LBJ FREEWAY, SUITE 675, DALLAS, TEXAS                75240
   (Address of principal executive offices)               (Zip Code)

                                 (972) 991-9090
              (Registrant's Telephone Number, including Area Code)

     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

MURRAY INCOME PROPERTIES I, LTD.
(A LIMITED PARTNERSHIP)
AND CONSOLIDATED JOINT VENTURE
CONSOLIDATED BALANCE SHEETS
-------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                                     June 30,           December 31,
                                                                       1998                 1997
                                                                  ---------------      ---------------
                                                                    (unaudited)
<S>                                                               <C>                  <C>            
  ASSETS
  Investment properties, at cost:
     Land                                                         $     6,232,801      $     6,232,801
     Buildings and improvements                                        20,377,765           20,319,183
                                                                  ---------------      ---------------
                                                                       26,610,566           26,551,984
     Less accumulated depreciation                                     10,200,725            9,779,632
                                                                  ---------------      ---------------
       Net investment properties                                       16,409,841           16,772,352

  Cash and cash equivalents                                             1,520,058            1,620,246
  Accounts and notes receivable,
     net of allowance of $2,766 and
     $5,655, in 1998 and 1997, respectively                               740,372              712,929
  Other assets, at cost, net of accumulated
     amortization of $547,822 and $512,307
     in 1998 and 1997, respectively                                       254,218              244,668
                                                                  ---------------      ---------------
                                                                  $    18,924,489      $    19,350,195
                                                                  ===============      ===============

  LIABILITIES AND PARTNERS' EQUITY
  Accounts payable                                                $        15,715      $        13,498
  Accrued property taxes                                                  133,589              195,500
  Security deposits                                                       184,538              183,609
                                                                  ---------------      ---------------
            Total liabilities                                             333,842              392,607
                                                                  ---------------      ---------------

  Minority interest in joint venture                                    1,356,136            1,391,212
                                                                  ---------------      ---------------

  Partners' equity:
     General Partners:
       Capital contributions                                                1,000                1,000
       Cumulative net earnings                                            228,251              217,606
       Cumulative cash distributions                                     (384,116)            (366,834)
                                                                  ---------------      ---------------
                                                                         (154,865)            (148,228)
                                                                  ---------------      ---------------

     Limited Partners (28,227 Interests):
       Capital contributions, net of offering costs                    24,570,092           24,570,092
       Cumulative net earnings                                         11,641,032           11,119,449
       Cumulative cash distributions                                  (18,821,748)         (17,974,937)
                                                                  ---------------      ---------------
                                                                       17,389,376           17,714,604
                                                                  ---------------      ---------------
            Total partners' equity                                     17,234,511           17,566,376
                                                                  ---------------      ---------------
                                                                  $    18,924,489      $    19,350,195
                                                                  ===============      ===============
 </TABLE>

See accompanying notes to consolidated financial statements.

                                       2
<PAGE>   3

MURRAY INCOME PROPERTIES I, LTD.
(A LIMITED PARTNERSHIP)
AND CONSOLIDATED JOINT VENTURE
CONSOLIDATED STATEMENTS OF EARNINGS
(UNAUDITED)
-------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                        Three Months Ended               Six Months Ended
                                                            June 30,                           June 30,
                                                 -------------------------------  -------------------------------
                                                     1998                1997           1998               1997   
                                                 -----------         ----------   --------------     ------------
<S>                                                  <C>              <C>              <C>              <C>        
 INCOME:
    Rental                                           $   775,385      $   799,158      $ 1,585,227      $ 1,630,111
    Interest                                              21,585           19,878           43,891           38,916
                                                     -----------      -----------      -----------      -----------
                                                         796,970          819,036        1,629,118        1,669,027
                                                     -----------      -----------      -----------      -----------

 EXPENSES:
    Depreciation                                         210,374          212,211          421,093          424,352
    Property operating                                   228,892          208,146          430,571          408,722
    General and administrative                            72,790           65,813          177,861          165,402
    Bad debts (recoveries), net                             (346)          (1,293)          (1,209)          (1,293)
                                                     -----------      -----------      -----------      -----------
                                                         511,710          484,877        1,028,316          997,183
                                                     -----------      -----------      -----------      -----------

      Earnings before minority interest                  285,260          334,159          600,802          671,844

      Minority interest in joint venture's
        earnings                                          30,953           32,652           68,574           70,872
                                                     -----------      -----------      -----------      -----------

      Net earnings                                   $   254,307      $   301,507      $   532,228      $   600,972
                                                     ===========      ===========      ===========      ===========

 Basic earnings per limited partnership interest     $      8.83      $     10.47      $     18.48      $     20.87
                                                     ===========      ===========      ===========      ===========
</TABLE>



See accompanying notes to consolidated financial statements.

                                       3
<PAGE>   4

MURRAY INCOME PROPERTIES I, LTD.
(A LIMITED PARTNERSHIP)
AND CONSOLIDATED JOINT VENTURE
CONSOLIDATED STATEMENTS OF CHANGES IN PARTNERS' EQUITY
(UNAUDITED)
-------------------------------------------------------------------------------


<TABLE>
<CAPTION>
                                           General            Limited
                                           Partners           Partners           Total
                                         ------------      ------------      ------------
<S>                                      <C>               <C>               <C>         

 SIX MONTHS ENDED JUNE 30, 1997:

    Balance at December 31, 1996         $   (137,548)     $ 18,237,930      $ 18,100,382
    Net earnings                               12,019           588,953           600,972
    Cash distributions                        (16,202)         (793,889)         (810,091)
                                         ------------      ------------      ------------
    Balance at June 30, 1997             $   (141,731)     $ 18,032,994      $ 17,891,263
                                         ============      ============      ============


 SIX MONTHS ENDED JUNE 30, 1998:

    Balance at December 31, 1997         $   (148,228)     $ 17,714,604      $ 17,566,376
    Net earnings                               10,645           521,583           532,228
    Cash distributions                        (17,282)         (846,811)         (864,093)
                                         ------------      ------------      ------------
    Balance at June 30, 1998             $   (154,865)     $ 17,389,376      $ 17,234,511
                                         ============      ============      ============
</TABLE>

See accompanying notes to consolidated financial statements.

                                       4
<PAGE>   5

MURRAY INCOME PROPERTIES I, LTD.
(A LIMITED PARTNERSHIP)
AND CONSOLIDATED JOINT VENTURE
CONSOLIDATED STATEMENTS OF CASH FLOWS
(UNAUDITED)
-------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                                            Six Months Ended
                                                                                June 30,
                                                                  ------------------------------------
                                                                       1998                    1997
                                                                  ---------------      ---------------
<S>                                                               <C>                  <C>            
 Cash flows from operating activities:
      Net earnings                                                $       532,228      $       600,972
      Adjustments to reconcile net earnings to net
        cash provided by operating activities:
          Bad debts (recoveries), net                                      (1,209)              (1,293)
          Depreciation                                                    421,093              424,352
          Amortization of other assets                                     35,515               36,384
          Minority interest in joint venture's earnings                    68,574               70,872
          Change in assets and liabilities:
            Accounts and notes receivable                                 (26,234)             (20,688)
            Other assets                                                  (45,065)             (39,639)
            Accounts payable                                                2,217                6,514
            Accrued property taxes and security deposits                  (60,982)            (102,184)
                                                                  ---------------      ---------------
               Net cash provided by operating activities                  926,137              975,290
                                                                  ---------------      ---------------

 Cash flows from investing activities:
      Additions to investment properties                                  (58,582)             (25,948)
                                                                  ---------------      ---------------

 Cash flows from financing activities:
      Distributions to minority interest in joint venture                (103,650)            (105,450)
      Cash distributions                                                 (864,093)            (810,091)
                                                                  ---------------      ---------------
             Net cash used in financing activities                       (967,743)            (915,541)
                                                                  ---------------      ---------------

 Net increase (decrease) in cash and cash equivalents                    (100,188)              33,801
 Cash and cash equivalents at beginning of period                       1,620,246            1,417,536
                                                                  ---------------      ---------------
 Cash and cash equivalents at end of period                       $     1,520,058      $     1,451,337
                                                                  ===============      ===============

</TABLE>


See accompanying notes to consolidated financial statements.

                                       5
<PAGE>   6

MURRAY INCOME PROPERTIES I, LTD.
(A LIMITED PARTNERSHIP)
AND CONSOLIDATED JOINT VENTURE
NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
-------------------------------------------------------------------------------

1.   BASIS OF ACCOUNTING

     The consolidated financial statements include the accounts of the
Partnership and Tower Place Joint Venture (85% owned by the Partnership). All
significant intercompany balances and transactions have been eliminated in
consolidation.

     The preparation of financial statements in conformity with generally
accepted accounting principles requires management to make estimates and
assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of income and expenses during the reporting
period. Actual results could differ from those estimates.

     Rental income is recognized as earned under the leases. Accordingly, the
Partnership accrues rental income for the full period of occupancy using the
straight line method over the related terms. At June 30, 1998 and December 31,
1997, $465,286 and $492,448, respectively, of accounts receivable related to
such accruals.

     Other assets consist primarily of deferred leasing costs which are
amortized using the straight line method over the lives of the related leases.

     Depreciation is provided over the estimated useful lives of the respective
assets using the straight line method. The estimated useful lives of the
buildings and improvements range from three to twenty-five years.

     The Partnership periodically reevaluates the propriety of the carrying
amounts of investment properties to determine whether current events and
circumstances warrant an adjustment to such carrying amounts. Such evaluations
are performed utilizing annual appraisals performed by independent appraisers as
well as internally developed estimates of expected undiscounted future cash
flows. In the event the carrying value of an individual property exceeds
expected future undiscounted cash flows, the property is written down to the
most recently appraised value. Since inception of the Partnership, none of the
Partnership's properties have required write downs.

     No provision for income taxes has been made as the liabilities for such
taxes are those of the individual Partners rather than the Partnership. The
Partnership files its tax return on the accrual basis used for Federal income
tax purposes.

     Earnings per limited partnership interest are based upon the limited
partnership interests outstanding at period-end and the net earnings allocated
to the Limited Partners in accordance with the Partnership Agreement.

     For purposes of reporting cash flows, the Partnership considers all
certificates of deposit and highly liquid debt instruments with original
maturities of three months or less to be cash equivalents.

                                       6
<PAGE>   7

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

     The following information relates to estimated fair values of the
Partnership's financial instruments as of June 30, 1998 and December 31, 1997.
For cash and cash equivalents, accounts and notes receivable, accounts payable,
accrued property taxes payable, and security deposits, the carrying amounts
approximate fair value because of the short maturity of these instruments.

2.   PARTNERSHIP AGREEMENT

     Pursuant to the terms of the Partnership Agreement, net profits or losses
of the Partnership and cash distributions are generally allocated 98% to the
Limited Partners and 2% to the General Partners. Cash distributions from the
sale or refinancing of a property are allocated as follows:

(a)      First, all Cash Distributions from Sales or Refinancings shall be
         allocated 99% to the Limited Partners and 1% to the Non-corporate
         General Partner until the Limited Partners have been returned their
         Original Invested Capital from Cash Distributions from Sales or
         Refinancings, plus their Preferred Return from Cash Distributions from
         Operations or Cash Distributions from Sales or Refinancings, or both.

(b)      Next, all Cash Distributions from Sales or Refinancings shall be
         allocated 1% to the Non-corporate General Partner and 99% to the
         Limited Partners and the General Partners. Such 99% will be allocated
         (i) first to the Corporate General Partner in an amount equal to any
         unpaid Cash Distributions from Operations subordinated to the Limited
         Partners' 7% non-cumulative annual return and (ii) thereafter, 80% to
         the Limited Partners and 20% to the General Partners.

         Cash Distributions from Sales or Refinancings (other than the 1% of
         Cash Distributions from Sales or Refinancings payable to the
         Non-corporate General Partner) payable to the General Partners shall be
         allocated 62 1/2% to the Non-corporate General Partner and 37 1/2% to
         the Corporate General Partner.

3.   INVESTMENT PROPERTIES

     The Partnership owns and operates Mountain View Plaza, a shopping center
located in Scottsdale, Arizona, and Castle Oaks Village, a shopping center
located in Castle Hills (San Antonio), Texas. In addition, the Partnership owns
an 85% interest in Tower Place Joint Venture, a joint venture which owns Tower
Place Festival Shopping Center located in Pineville (Charlotte), North Carolina.
The remaining 15% interest in the joint venture is owned by Murray Income
Properties II, Ltd. ("MIP II"), an affiliated real estate limited partnership.
The Tower Place Joint Venture Agreement provides that the Partnership will share
profits, losses, and cash distributions according to the Partnership's 85%
ownership interest in the joint venture.

4.   OTHER

     Information furnished in this interim report reflects all adjustments
consisting of normal recurring adjustments, which, in the opinion of management,
are necessary to reflect a fair presentation of the results for the periods
presented.

                                       7
<PAGE>   8

     The financial information included in this interim report as of June 30,
1998 and for the three and six months ended June 30, 1998 and 1997 has been
prepared by management without audit by independent public accountants who do
not express an opinion thereon. The Partnership's annual report contains audited
consolidated financial statements. The notes to the consolidated financial
statements in the Partnership's 1997 annual report are an integral part of the
consolidated financial statements presented herein.

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

Liquidity and Capital Resources

     As of June 30, 1998, the Partnership had cash and cash equivalents of
$1,520,058. Such amounts represent cash generated from operations and working
capital reserves.

     Rental income from leases with escalating rental rates is accrued using the
straight line method over the related lease terms. At June 30, 1998 and December
31, 1997, $465,286 and $492,448, respectively, of accounts receivable related to
such accruals. Accounts receivable also consist of tenant receivables,
receivables for rent collected (but not yet remitted by the property management
companies managing the properties), and interest receivable on short-term
investments. The increase in accounts receivable of $26,234 (exclusive of bad
debts and recoveries) from December 31, 1997 to June 30, 1998 is primarily due
to an increase in receivables for rent collected (but not yet remitted by the
property management company) at each of the Partnership's properties, offset by
a decrease in receivables related to the accruals described above at each of the
Partnership's properties. As of June 30, 1998 and December 31, 1997, the
Partnership had allowances of $2,766 and $5,655 respectively, for uncollectible
accounts receivable.

     The decrease of $61,911 in accrued property taxes from December 31, 1997 to
June 30, 1998 is primarily due to the payment of 1997 property taxes for the
Partnership's properties.

     During the three months ended June 30, 1998, the Partnership made Cash
Distributions from Operations totaling $432,047, (which was reduced by $23,455
related to 1997 North Carolina state income taxes paid on behalf of the partners
in connection with the operation of Tower Place Joint Venture) related to the
three month period ended March 31, 1998. Subsequent to June 30, 1998, the
Partnership made Cash Distributions from Operations of $432,046 relating to the
three months ended June 30, 1998. The distributed funds were derived from the
net cash flow generated from operations of the Partnership's properties and from
interest earned, net of administrative expenses, on funds invested in short-term
money market instruments.

     Future liquidity is currently expected to result from cash generated from
the operations of the Partnership's properties (which could be affected
negatively in the event of weakened occupancies, and/or rental rates), interest
earned on funds invested in short-term money market instruments and ultimately
through the sale of the Partnership's properties.

                                       8
<PAGE>   9

Results of Operations

     Rental income decreased $44,884 for the six months ended June 30, 1998 as
compared to the same period in 1997. The following information details the
rental income generated, bad debt expense incurred, and average occupancy for
the periods shown for each of the Partnership's properties.

<TABLE>
<CAPTION>
                                                     Three Months Ended            Six Months Ended
                                                         June 30,                      June 30,
                                              -------------------------------------------------------------
                                                 1998             1997            1998              1997
                                              ----------       ----------       ----------       ----------
<S>                                           <C>              <C>              <C>              <C>
 Mountain View Plaza Shopping Center

    Rental income                             $  236,603       $  260,023       $  468,722       $  517,429
    Bad debt expense                                 510              -0-              510              -0-
    Average occupancy                                 98%             100%              98%             100%

 Castle Oaks Village Shopping Center

    Rental income                             $  106,999       $  104,197       $  217,797       $  209,354
    Bad debt expense (recovery)                      -0-           (2,253)          (1,474)          (2,253)
    Average occupancy                                 92%              91%              92%              91%

 Tower Place Festival Shopping Center

    Rental income                             $  431,783       $  434,938       $  898,708       $  903,328
    Bad debt expense (recovery)                     (856)             960             (245)             960
    Average occupancy                                 98%              98%              98%              98%
</TABLE>

     Rental income at Mountain View Plaza in Scottsdale, Arizona decreased
$48,707 for the six months ended June 30, 1998 as compared to the same period in
1997 due to lower tenant reimbursements for common area maintenance costs and
real estate taxes.

     Occupancy at Mountain View averaged 98% during the quarter ended June 30,
1998, a one percent increase over the previous quarter. One tenant who occupies
1,033 square feet renewed its lease for two years. A tenant who occupied 1,353
square feet and signed a lease to expand into an additional 880 square feet took
possession of this space in April. Wild Oats Markets, who occupied 19,359 square
feet, closed its store in November, 1997. While this space has remained vacant,
Wild Oats has continued to pay rent and abide by the terms of its lease.
Management and Wild Oats Markets are aggressively pursuing a replacement tenant
for this space.

     Rental income at Castle Oaks Village in Castle Hills (San Antonio), Texas
increased $8,443 for the six months ended June 30, 1998 as compared to the same
period in 1997 primarily due to an increase in rental rates and higher tenant
reimbursements for common area maintenance costs and real estate taxes.

     Occupancy at Castle Oaks averaged 92% during the quarter ended June 30,
1998, unchanged from the previous quarter.

     Rental income at Tower Place in Pineville (Charlotte), North Carolina
decreased $4,620 for the six months ended June 30, 1998 as compared to the same
period in 1997, with increases in base rent

                                       9
<PAGE>   10



being offset by decreases in tenant reimbursements for common area maintenance
costs and percentage rent received.

     Occupancy at Tower Place averaged 98% during the quarter ended June 30,
1998, unchanged from the previous quarter. One tenant who occupies 1,400 square
feet renewed its lease for two years, and another tenant who occupies 1,120
square feet renewed its lease for one year. A tenant who occupied 2,700 square
feet and had signed a lease to expand into an additional 1,050 square feet took
possession of this space in May. One tenant who occupied 1,600 square feet
vacated its space upon expiration of its lease. Repairs were completed to one of
the buildings where ground water had been seeping into a movie theater after
heavy rains.

     Depreciation is provided over the estimated useful lives of the respective
assets using the straight line method. The estimated useful lives of the
buildings and improvements range from three to twenty-five years.

     Property operating expenses consist primarily of real estate taxes,
property management fees, insurance costs, utility costs, repair and maintenance
costs, leasing and promotion costs, and amortization of deferred leasing costs.
Property operating expenses increased $21,849 for the six months ended June 30,
1998 as compared to the same period in 1997 primarily because of increased
repair and maintenance costs at Tower Place, higher leasing and promotion costs
and legal costs at Mountain View Plaza and higher real estate taxes at Tower
Place and Castle Oaks. Mountain View Plaza's total operating expenses increased
primarily because of increases in leasing and promotion expenses and legal
costs. Castle Oak's total operating expenses increased with higher utilities,
repair and maintenance costs and real estate taxes being offset by lower
landscaping costs and insurance costs. Tower Place's total operating expenses
increased with higher repair and maintenance costs and real estate taxes being
offset by lower leasing and promotion costs.

     General and administrative expenses incurred are related to legal and
accounting expenses, rent, investor services costs, salaries and benefits and
various other costs required for the administration of the Partnership,
including reimbursements of shared direct operating costs to Murray Income
Properties II, Ltd. General and administrative expenses increased $12,459 for
the six months ended June 30, 1998 as compared to the same period in 1997
primarily due to increases in investor services costs and salaries and benefits.

                                       10
<PAGE>   11

PART II.  OTHER INFORMATION

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

     (a)      Exhibits:

              3a     Agreement of Limited Partnership of Murray Income
                     Properties Ltd. 84. Reference is made to Exhibit A of the
                     Prospectus dated May 31, 1984 contained in Amendment No. 2
                     to Partnership's Form S-11 Registration Statement. (File
                     No. 2-90016)

              3b     Amended and Restated Certificate and Agreement of Limited
                     Partnership dated as of May 23, 1984. Reference is made to
                     Exhibit 3b to the 1989 Annual Report on Form 10-K filed
                     with the Securities and Exchange Commission on March 31,
                     1990. (File No. 0-14105)

              3c     Amended and Restated Certificate and Agreement of Limited
                     Partnership dated as of June 25, 1984. Reference is made to
                     Exhibit 3c to the 1989 Annual Report on Form 10-K filed
                     with the Securities and Exchange Commission on March 31,
                     1990. (File No. 0-14105)

              3d     Amended and Restated Certificate and Agreement of Limited
                     Partnership dated as of November 27, 1984. Reference is
                     made to Exhibit 3d to the 1989 Annual Report on Form 10-K
                     filed with the Securities and Exchange Commission on March
                     31, 1990. (File No. 0-14105)

              3e     Amended and Restated Certificate and Agreement of Limited
                     Partnership dated as of April 1, 1985. Reference is made to
                     Exhibit 3e to the 1989 Annual Report on Form 10-K filed
                     with the Securities and Exchange Commission on March 31,
                     1990. (File No. 0-14105)

              3f     Amended and Restated Certificate and Agreement of Limited
                     Partnership dated as of November 15, 1989. Reference is
                     made to Exhibit 3f to the 1989 Annual Report on Form 10-K
                     filed with the Securities and Exchange Commission on March
                     31, 1990. (File No. 0-14105)

              3g     Amended and Restated Certificate and Agreement of Limited
                     Partnership dated as of January 10, 1990. Reference is made
                     to Exhibit 3g to the 1989 Annual Report on Form 10-K filed
                     with the Securities and Exchange Commission on March 31,
                     1990. (File No. 0-14105)

              27     Financial Data Schedule.  Filed herewith.

              99a    Glossary, as contained in the Prospectus dated May 31, 1984
                     filed as part of Amendment No. 2 to Registrant's Form S-11
                     Registration Statement. (File No. 2-90016) Filed herewith.

              99b    Article XIII of the Agreement of Limited Partnership as
                     contained in the Prospectus dated May 31, 1984 filed as
                     part of the Amendment No. 2 to Registrant's Form S-11
                     Registration Statement. (File No. 2-90016) Filed herewith.
  
                                       11
<PAGE>   12

              99c    Amendment number nine to the Agreement of Limited
                     Partnership contained in the Proxy Statement dated October
                     11, 1989. Filed herewith.

              99d    Management Compensation as contained in the Prospectus
                     (Pages 10 through 17) dated May 31, 1984 filed as part of
                     Amendment No. 2 to Registrant's Form S-11 Registration
                     Statement. (File No. 2-90016) Filed herewith.

     (b)      Reports on Form 8-K filed during the quarter ended June 30, 1998:

              None

                                       12
<PAGE>   13



                                   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.

                                        MURRAY INCOME PROPERTIES I, LTD.

                                        By: Murray Realty Investors VIII, Inc.
                                            A General Partner



Date: August 10, 1998                   By:      /s/ Mitchell Armstrong
                                            ------------------------------
                                            Mitchell Armstrong
                                            President
                                            Chief Financial Officer

                                       13
<PAGE>   14

                                INDEX TO EXHIBITS
<TABLE>
<CAPTION>
  Document
   Number       Description
  --------      -----------
<S>             <C>
     3a         Agreement of Limited Partnership of Murray Income Properties
                Ltd. 84. Reference is made to Exhibit A of the Prospectus dated
                May 31, 1984 contained in Amendment No. 2 to Partnership's Form
                S-11 Registration Statement. (File No. 2-90016)

     3b         Amended and Restated Certificate and Agreement of Limited
                Partnership dated as of May 23, 1984. Reference is made to
                Exhibit 3b to the 1989 Annual Report on Form 10-K filed with the
                Securities and Exchange Commission on March 31, 1990. (File No.
                0-14105)

     3c         Amended and Restated Certificate and Agreement of Limited
                Partnership dated as of June 25, 1984. Reference is made to
                Exhibit 3c to the 1989 Annual Report on Form 10-K filed with the
                Securities and Exchange Commission on March 31, 1990. (File No.
                0-14105)

     3d         Amended and Restated Certificate and Agreement of Limited
                Partnership dated as of November 27, 1984. Reference is made to
                Exhibit 3d to the 1989 Annual Report on Form 10-K filed with the
                Securities and Exchange Commission on March 31, 1990. (File No.
                0-14105)

     3e         Amended and Restated Certificate and Agreement of Limited
                Partnership dated as of April 1, 1985. Reference is made to
                Exhibit 3e to the 1989 Annual Report on Form 10-K filed with the
                Securities and Exchange Commission on March 31, 1990. (File No.
                0-14105)

     3f         Amended and Restated Certificate and Agreement of Limited
                Partnership dated as of November 15, 1989. Reference is made to
                Exhibit 3f to the 1989 Annual Report on Form 10-K filed with the
                Securities and Exchange Commission on March 31, 1990. (File No.
                0-14105)

     3g         Amended and Restated Certificate and Agreement of Limited
                Partnership dated as of January 10, 1990. Reference is made to
                Exhibit 3g to the 1989 Annual Report on Form 10-K filed with the
                Securities and Exchange Commission on March 31, 1990. (File No.
                0-14105)

     27         Financial Data Schedule.  Filed herewith.

     99a        Glossary, as contained in the Prospectus dated May 31, 1984
                filed as part of Amendment No. 2 to Registrant's Form S-11
                Registration Statement. (File No. 2-90016) Filed herewith.

     99b        Article XIII of the Agreement of Limited Partnership as
                contained in the Prospectus dated May 31, 1984 filed as part of
                the Amendment No. 2 to Registrant's Form S-11 Registration
                Statement. (File No. 2-90016) Filed herewith.

     99c        Amendment number nine to the Agreement of Limited Partnership
                contained in the 
</TABLE>

                                       14
<PAGE>   15

<TABLE>
<S>             <C>
                Proxy Statement dated October 11, 1989. Filed
                herewith.

     99d        Management Compensation as contained in the Prospectus (Pages 10
                through 17) dated May 31, 1984 filed as part of Amendment No. 2
                to Registrant's Form S-11 Registration Statement. (File No.
                2-90016) Filed herewith.
</TABLE>

                                       15