<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM 10-Q


              [X] QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF THE
       SECURITIES EXCHANGE ACT OF 1934 FOR THE QUARTER ENDED JUNE 30, 1998
                                                             -------------


                          Commission File Number 1-9525
                                                 ------



                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
             ------------------------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)




          NEVADA                                                  75-2615944
-------------------------------                              -------------------
(State or Other Jurisdiction of                               (I.R.S. Employer
 Incorporation or Organization)                              Identification No.)



    10670 North Central Expressway, Suite 300, Dallas, Texas,     75231
    ----------------------------------------------------------------------
    (Address of Principal Executive Offices)                    (Zip Code)



                                 (214) 692-4700
                         -------------------------------
                         (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    .
                                       ---     ---   



Common Stock, $.01 par value                                1,522,531
----------------------------                      ------------------------------
         (Class)                                  (Outstanding at July 31, 1998)

                                        1

<PAGE>   2



                          PART I. FINANCIAL INFORMATION


ITEM 1.  FINANCIAL STATEMENTS

The accompanying Consolidated Financial Statements have not been audited by
independent certified public accountants, but in the opinion of the management
of Income Opportunity Realty Investors, Inc. (the "Company"), all adjustments
(consisting of normal recurring accruals) necessary for a fair presentation of
the Company's consolidated financial position, consolidated results of
operations and consolidated cash flows at the dates and for the periods
indicated, have been included.

                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                           CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                                                    June 30,  December 31,
                                                                                                      1998       1997
                                                                                                    --------  ------------
                                                                                                    (dollars in thousands)
<S>                                                                                                 <C>         <C>    
                                                   Assets
                                                   ------
Notes and interest receivable
   Performing .................................................................................     $ 2,015     $ 2,010

Real estate held for investment, net of
   accumulated depreciation ($6,233 in 1998 and
   $5,211 in 1997) ............................................................................      82,983      81,914

Investment in partnerships ....................................................................       1,626       1,762
Cash and cash equivalents .....................................................................         420       1,145
Other assets (including $117 in 1998 and $302 in
   1997 from affiliates) ......................................................................       3,198       3,478
                                                                                                    -------     -------
                                                                                                    $90,242     $90,309
                                                                                                    =======     =======

                                    Liabilities and Stockholders' Equity
                                    ------------------------------------
Liabilities
Notes and interest payable ....................................................................     $60,921     $61,323
Other liabilities (including $1,620 in 1998 and
   $468 in 1997 to affiliates) ................................................................       4,562       3,855
                                                                                                    -------     -------
                                                                                                     65,483      65,178

Commitments and contingencies

Stockholders' equity
Common Stock, $.01 par value;
   authorized, 10,000,000 shares; issued and
   outstanding, 1,522,531 shares in 1998 and
   1,519,888 in 1997 ..........................................................................          15          15
Paid-in capital ...............................................................................      64,833      64,804
Accumulated distributions in excess of accumulated
   earnings ...................................................................................     (40,089)    (39,688)
                                                                                                    -------     -------
                                                                                                     24,759      25,131
                                                                                                    -------     -------
                                                                                                    $90,242     $90,309
                                                                                                    =======     =======
</TABLE>


              The accompanying notes are an integral part of these
                       Consolidated Financial Statements.

                                        2

<PAGE>   3



                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                      CONSOLIDATED STATEMENTS OF OPERATIONS




<TABLE>
<CAPTION>
                                                                            For the Three Months           For the Six Months
                                                                               Ended June 30,                Ended June 30,
                                                                         -------------------------     -------------------------
                                                                            1998           1997           1998           1997
                                                                         ----------     ----------     ----------     ----------
                                                                                (dollars in thousands, except per share)
<S>                                                                      <C>            <C>            <C>            <C>       
INCOME
   Rents ..............................................................  $    3,600     $    2,893     $    7,190     $    5,585
   Interest ...........................................................          62             73            125            142
                                                                         ----------     ----------     ----------     ----------

                                                                              3,662          2,966          7,315          5,727



EXPENSES
   Property operations ................................................       1,494          1,225          2,955          2,565
   Interest ...........................................................       1,423            901          2,829          1,778
   Depreciation .......................................................         518            340          1,022            705
   Advisory fee to affiliate ..........................................         167            123            335            246
   Net income fee to affiliate ........................................           4             94              4            218
   General and administrative .........................................         172            172            388            437
                                                                         ----------     ----------     ----------     ----------
                                                                              3,778          2,855          7,533          5,949
                                                                         ----------     ----------     ----------     ----------

Income (loss) from operations .........................................        (116)           111           (218)          (222)

Equity in income of
   partnerships .......................................................         248             29            261             46
Gain on sale of real estate ...........................................          --          1,473             --          3,322
                                                                         ----------     ----------     ----------     ----------

Net income ............................................................  $      132     $    1,613     $       43     $    3,146
                                                                         ==========     ==========     ==========     ==========




Earnings Per Share
   Net income .........................................................  $      .09     $     1.06     $      .03     $     2.07
                                                                         ==========     ==========     ==========     ==========




Weighted average Common shares
   used in computing earnings
   per share ..........................................................   1,520,481      1,519,888      1,520,186      1,519,888
                                                                         ==========     ==========     ==========     ==========
</TABLE>






              The accompanying notes are an integral part of these
                       Consolidated Financial Statements.

                                        3

<PAGE>   4



                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                 CONSOLIDATED STATEMENT OF STOCKHOLDERS' EQUITY
                     For the Six Months Ended June 30, 1998


<TABLE>
<CAPTION>
                                                                          Accumulated
                                                                         Distributions
                                     Common Stock                        in Excess of
                               -----------------------      Paid-In       Accumulated  Stockholders'
                                 Shares        Amount       Capital         Earnings     Equity
                               ---------     ---------     ---------     ------------- -------------
                                                            (dollars in thousands)
<S>                            <C>           <C>           <C>           <C>            <C>      
Balance, January 1, 1998 ....  1,519,888     $      15     $  64,804     $  (39,688)    $  25,131



Sale of Common Stock under
   dividend reinvestment
   plan .....................      2,643          --              29           --              29

Dividends ($.30 per share) ..       --            --            --             (444)         (444)


Net income ..................       --            --            --               43            43
                               ---------     ---------     ---------     ----------     ---------



Balance, June 30, 1998 ......  1,522,531     $      15     $  64,833     $  (40,089)    $  24,759
                               =========     =========     =========     ==========     =========
</TABLE>








              The accompanying notes are an integral part of these
                       Consolidated Financial Statements.

                                        4

<PAGE>   5



                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS



<TABLE>
<CAPTION>
                                                                                            For the Six Months
                                                                                              Ended June 30,
                                                                                  -------------------------------------
                                                                                        1998                 1997
                                                                                  ----------------     ----------------
                                                                                          (dollars in thousands)
<S>                                                                               <C>                  <C>             
Cash Flows from Operating Activities
   Rents collected ..........................................................     $          7,251     $          5,330
   Interest collected .......................................................                  119                  136
   Interest paid ............................................................               (2,706)              (1,582)
   Payments for property operations .........................................               (3,223)              (2,066)
   Advisory and net income fee paid to affiliate ............................                 (400)                (374)
   General and administrative expenses paid .................................                 (700)                (589)
   Other ....................................................................                   18                  479
                                                                                  ----------------     ----------------

      Net cash provided by operating activities .............................                  359                1,334


Cash Flows from Investing Activities
   Acquisition of real estate ...............................................                 --                (30,659)
   Proceeds from sale of real estate ........................................                 --                 21,989
   Real estate improvements .................................................               (2,090)                (321)
   Funding of equity partnerships ...........................................                   (2)                (221)
   Distributions from equity partnerships'
      investing cash flow ...................................................                  399                 --
                                                                                  ----------------     ----------------

      Net cash (used in) investing activities................................               (1,693)              (9,212)


Cash Flows from Financing Activities
   Payments on notes payable ................................................                 (461)             (15,560)
   Proceeds from notes payable ..............................................                 --                 21,640
   Deferred borrowing costs .................................................                 --                    (15)
   Sale of Common Stock under dividend reinvestment
      plan ..................................................................                   29                 --
   Dividends to stockholders ................................................                 (444)                (304)
   Advances from advisor ....................................................                1,485                   31
                                                                                  ----------------     ----------------

      Net cash provided by financing activities .............................                  609                5,792


Net (decrease) in cash and cash equivalents..................................                 (725)              (2,086)
Cash and cash equivalents, beginning of period ..............................                1,145                3,186
                                                                                  ----------------     ----------------

Cash and cash equivalents, end of period ....................................     $            420     $          1,100
                                                                                  ================     ================
</TABLE>





              The accompanying notes are an integral part of these
                       Consolidated Financial Statements.

                                        5

<PAGE>   6



                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS





<TABLE>
<CAPTION>
                                                                                    For the Six Months
                                                                                      Ended June 30,
                                                                                    ------------------
                                                                                     1998        1997
                                                                                    ------      ------
                                                                                  (dollars in thousands)
<S>                                                                                  <C>        <C>   
Reconciliation of net income to net cash
   provided by operating activities
Net income .....................................................................     $   43     $3,146
Adjustments to reconcile net income to net cash
   provided by operating activities
   (Gain) on sale of real estate ...............................................        --      (3,322)
   Depreciation and amortization ...............................................      1,081        765
   Equity in (income) of partnerships ..........................................       (261)       (46)
   (Increase) decrease in other assets .........................................        218       (143)
   Increase in interest payable ................................................         58        130
   Increase (decrease) in other liabilities ....................................       (780)       804
                                                                                     ------     ------

      Net cash provided by operating activities ................................     $  359     $1,334
                                                                                     ======     ======




Schedule of noncash investing and financing
   activities

Notes payable from purchase of real estate .....................................     $ --       $3,470
</TABLE>





              The accompanying notes are an integral part of these
                       Consolidated Financial Statements.

                                        6

<PAGE>   7



                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


NOTE 1.        BASIS OF PRESENTATION

The accompanying Consolidated Financial Statements have been prepared in
accordance with generally accepted accounting principles for interim financial
information and with the instructions to Form 10-Q and Article 10 of Regulation
S-X. Accordingly, they do not include all of the information and notes required
by generally accepted accounting principles for complete financial statements.
Operating results for the six month period ended June 30, 1998 are not
necessarily indicative of the results that may be expected for the year ending
December 31, 1998. For further information, refer to the Consolidated Financial
Statements and notes thereto included in the Company's Annual Report on Form
10-K for the year ended December 31, 1997 (the "1997 Form 10-K").

Certain balances for 1997 have been reclassified to conform to the 1998
presentation.

NOTE 2.        INVESTMENT IN EQUITY METHOD REAL ESTATE ENTITIES

The Company owns a 36.3% general partner interest in Tri-City Limited
Partnership ("Tri-City"), which owned five properties in Texas. In May 1998,
Tri-City sold two of its apartment complexes for a total of $3.3 million in
cash. Tri-City received net cash of $1.4 million after the payoff of $1.9
million in existing mortgage debt and the payment of various closing costs
associated with the sale. The Company received a distribution of $399,000 of
such net cash. Tri-City paid a real estate brokerage commission of $119,000 to
Carmel Realty, Inc., an affiliate of Basic Capital Management, Inc., the
Company's advisor, based on the $3.3 million sales price of the properties.
Tri-City recognized a gain of $496,000 on the sale of which the Company's equity
share was $180,000.

NOTE 3.        COMMITMENTS AND CONTINGENCIES

The Company is involved in various lawsuits arising in the ordinary course of
business. The Company's management is of the opinion that the outcome of these
lawsuits will have no material impact on the Company's financial condition,
results of operations or liquidity.

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

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

Introduction

Income Opportunity Realty Investors, Inc. (the "Company") invests in equity
interests in real estate through acquisitions, leases and partnerships, and has
invested in mortgage loans on real estate, including first, wraparound, and
junior mortgage loans. The Company is the successor to a California business
trust organized on December 14, 1984 which commenced operations on April 10,
1985.

                                        7

<PAGE>   8



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

Liquidity and Capital Resources

Cash and cash equivalents at June 30, 1998 were $420,000, compared with $1.1
million at December 31, 1997. The Company's principal sources of cash have been
and will continue to be property operations, proceeds from property sales,
financings and refinancings and, to a lesser extent, distributions from
partnerships.

The Company's cash flow from property operations (rents collected less payments
for property operating expenses) increased from $3.3 million for the six months
ended June 30, 1997 to $4.0 million for the six months ended June 30, 1998. This
increase is primarily due to the Company having acquired eight income producing
properties in 1997. The Company's management believes that this trend will
continue for the remainder of 1998 as the Company continues to benefit from the
acquired properties and increased rental rates at both the Company's apartments
and commercial properties and increased occupancy at its commercial properties.

In August 1998, the Company's one mortgage note receivable, with a principal
balance of $2.0 million at June 30, 1998, matures. The Company expects to
collect such note at maturity.

In the first six months of 1998, the Company paid quarterly dividends of $.30
per share or a total of $444,000 and sold 2,643 shares of its Common Stock,
through its dividend reinvestment program for a total of $29,000.

The Company's management reviews the carrying values of the Company's properties
and mortgage note receivable at least annually and whenever events or a change
in circumstances indicate that impairment may exist. Impairment is considered to
exist if, in the case of a property, the future cash flow from the property
(undiscounted and without interest) is less than the carrying amount of the
property. For notes receivable impairment is considered to exist if it is
probable that all amounts due under the terms of the note will not be collected.
In those instances where impairment is found to exist, a provision for loss is
recorded by a charge against earnings. The Company's mortgage note receivable
review includes an evaluation of the collateral property securing such note. The
property review generally includes selective property inspections, a review of
the property's current rents compared to market rents, a review of the
property's expenses, a review of maintenance requirements, a review of the
property's cash flow, discussions with the manager of the property and a review
of properties in the surrounding area.

Results of Operations

For the three and six months ended June 30, 1998, the Company had net income of
$132,000 and $43,000 as compared with net income of $1.6 million and $3.1
million in the corresponding periods in 1997. Net income for the three and six
months ended June 30, 1997 included gains

                                        8

<PAGE>   9



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

Results of Operations (Continued)

on sale of real estate of $1.5 million and $3.3 million, respectively.
Fluctuations in this and other components of the Company's revenues and expenses
between the 1997 and 1998 periods are discussed below.

Rents in the three and six months ended June 30, 1998 were $3.6 million and $7.2
million as compared to $2.9 million and $5.6 million in the corresponding
periods in 1997. Of the increase, $1.4 million and $3.3 million for the three
and six months ended June 30, 1998 is due to eight properties being acquired
during 1997. This increase was partially offset by a decrease of $697,000 and
$1.7 million for the three and six months ended June 30, 1998 due to the sale of
three of the Company's apartment complexes in 1997. Rents for the remainder of
1998 are expected to increase as the Company continues to benefit from the
operations of the properties acquired in the second half of 1997 and increased
rental rates at both the Company's apartments and commercial properties and
increased occupancy at its commercial properties.

Property operations expense in the three and six months ended June 30, 1998 was
$1.5 million and $3.0 million as compared to $1.2 million and $2.6 million in
the corresponding periods in 1997. Of the increase, $772,000 and $1.5 million
for the three and six months ended June 30, 1998, is due to the acquisition of
eight properties during 1997. This increase was partially offset by a decrease
of $450,000 and $1.1 million for the three and six months ended June 30, 1998
due to the sale of three of the Company's apartment complexes in 1997.

Interest income of $62,000 and 125,000 in the three and six months ended June
30, 1998 approximated the $73,000 and $142,000 in the corresponding periods in
1997. Interest income for the remainder of 1998 is expected to be minimal due to
the expected August 1998 payoff of the Company's one mortgage note receivable.

Interest expense increased to $1.4 million and $2.8 million in the three and six
months ended June 30, 1998 compared to the $901,000 and $1.8 million in the
corresponding periods in 1997. Of this increase, $562,000 and $1.3 million for
the three and six months ended June 30, 1998 was due to the debt incurred or
assumed on six of the eight properties acquired during 1997, and $117,000 and
$234,000 for the three and six months ended June 30, 1998 was due to the
refinancing of a property. These increases were partially offset by a decrease
of $153,000 and $444,000 for the three and six months ended June 30, 1998 due to
the sale of three of the Company's apartment complexes during 1997. Interest
expense for the remainder of 1998 is expected to be comparable to that of the
first and second quarters of 1998.

Depreciation expense increased to $518,000 and $1.0 million for the three and
six months ended June 30, 1998 compared to $340,000 and $705,000 in the
corresponding periods in 1997.  The increase is due to the eight properties
acquired during 1997 partially offset by the sale of three of the Company's
apartment complexes in 1997.  Depreciation

                                        9

<PAGE>   10



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


Results of Operations (Continued)

expense is expected to remain constant for the remainder of 1998 as the Company
does not expect to acquire additional properties during 1998.

Advisory fee expense increased to $167,000 and $335,000 in the three and six
months ended June 30, 1998 compared to $123,000 and $246,000 for the
corresponding periods in 1997. The increase is due to an increase in the
Company's gross assets, the basis for such fee. Advisory fee expense is expected
to remain constant for the remainder of 1998 as the Company does not expect to
acquire additional properties during 1998.

Net income fee in the three and six months ended June 30, 1998 was $4,000 and
$4,000 as compared to $94,000 and $218,000 in the corresponding periods in 1997.
Such fee is payable to the Company's advisor based on 7.5% of the Company's net
income.

General and administrative expense of $172,000 and $388,000 in the three and six
months ended June 30, 1998 was comparable to the $172,000 and $437,000 in the
corresponding periods in 1997. General and administrative expense for the
remainder of 1998 is expected to be comparable to that of the first and second
quarters of 1998.

Tax Matters

As more fully discussed in the Company's 1997 Form 10-K, the Company has elected
and, in management's opinion, qualified, to be taxed as a real estate investment
trust ("REIT"), as defined under Sections 856 through 860 of the Internal
Revenue Code of 1986, as amended, (the "Code"). To continue to qualify for
federal taxation as a REIT under the Code, the Company is required to hold at
least 75% of the value of its total assets in real estate assets, government
securities, cash and cash equivalents at the close of each quarter of each
taxable year. The Code also requires a REIT to distribute at least 95% of its
REIT taxable income plus 95% of its net income from foreclosure property, all as
defined in Section 857 of the Code, on an annual basis to shareholders.

Inflation

The effects of inflation on the Company's operations are not quantifiable.
Revenues from property operations generally fluctuate proportionately with
inflationary increases and decreases in housing costs. Fluctuations in the rate
of inflation also affect the sales value of properties and, correspondingly, the
ultimate gain to be realized by the Company from property sales. To the effect
that inflation affects interest rates, the Company's earnings from short-term
investments and the cost of the new financings as well as the cost of its
variable note financing will be affected. Inflation also has an effect on the
Company's earnings from short-term investments.

                                       10

<PAGE>   11



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

Environmental Matters

Under various federal, state and local environmental laws, ordinances and
regulations, the Company may be potentially liable for removal or remediation
costs, as well as certain other potential costs, relating to hazardous or toxic
substances (including governmental fines and injuries to persons and property)
where property-level managers have arranged for the removal, disposal or
treatment of hazardous or toxic substances. In addition, certain environmental
laws impose liability for release of asbestos-containing materials into the air,
and third parties may seek recovery from the Company for personal injury
associated with such materials.

The Company's management is not aware of any environmental liability relating to
the above matters that would have a material adverse effect on the Company's
business, assets or results of operations.

Year 2000

The Company's advisor has advised the Company that its current computer software
has been certified by the Information Technology Association of America ("ITAA")
as year 2000 compliant. The Company's advisor has also advised the Company that
it has recently received and plans to install in the third quarter of 1998 the
ITAA certified year 2000 compliant operating system for its computer hardware.


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


                           PART II. OTHER INFORMATION


ITEM 1.        LEGAL PROCEEDINGS

Olive Litigation. In February 1990, the Company, together with Continental
Mortgage and Equity Trust ("CMET"), National Income Realty Trust and
Transcontinental Realty Investors, Inc. ("TCI"), three real estate entities
with, at the time, the same officers, directors or trustees and advisor as the
Company, entered into a settlement of a class and derivative action entitled
Olive et al. v. National Income Realty Trust et al. pending before the United
States District Court for the Northern District of California and relating to
the operation and management of each of the entities (the "Olive Litigation").
On April 23, 1990, the Court granted final approval of the terms of a
Stipulation of Settlement.

On May 4, 1994, the parties entered into a Modification of Stipulation of
Settlement dated April 27, 1994 (the "Olive Modification") that settled
subsequent claims of breaches of the settlement that were asserted by the
plaintiffs and that modified certain provisions of the

                                       11

<PAGE>   12



ITEM 1.        LEGAL PROCEEDINGS (Continued)

April 1990 settlement. The Olive Modification was preliminarily approved by the
Court on July 1, 1994, and final court approval was entered on December 12,
1994. The effective date of the Olive Modification was January 11, 1995.

The Court retained jurisdiction to enforce the Olive Modification, and during
August and September 1996, the Court held evidentiary hearings to assess
compliance with the terms of the Olive Modification by various parties. The
Court issued no ruling or order with respect to the matters addressed at the
hearings.

Separately, in 1996, legal counsel for the plaintiffs notified the Company's
Board of Directors that he intended to assert that certain actions taken by the
Board of Directors breached the terms of the Olive Modification. On January 27,
1997, the parties entered into an Amendment to the Olive Modification effective
January 9, 1997 (the "Olive Amendment"), which was submitted to the Court for
approval on January 29, 1997. The Olive Amendment provides for the settlement of
all matters raised at the evidentiary hearings and by plaintiffs' counsel in his
notices to the Company's Board of Directors. On May 2, 1997, a hearing was held
for the Court to consider approval of the Olive Amendment. As a result of the
hearing, the parties entered into a revised Olive Amendment. The Court issued an
order approving the Olive Amendment on July 3, 1997.

The Olive Amendment provides for the addition of four new unaffiliated members
to the Company's Board of Directors and sets forth new requirements for the
approval of any transactions with certain affiliates until April 28, 1999. In
addition, the Company, CMET, TCI and their shareholders released the defendants
from any claims relating to the plaintiffs' allegations and matters which were
the subject of the evidentiary hearings. The plaintiffs' allegations of any
breaches of the Olive Modification shall be settled by mutual agreement of the
parties or, lacking such agreement, by an arbitration proceeding.

Under the Olive Amendment, all shares of the Company owned by Gene E. Phillips
or any of his affiliates shall be voted at all stockholder meetings of the
Company held until April 28, 1999 in favor of all new Board members added under
the Olive Amendment. The Olive Amendment also requires that, until April 28,
1999, all shares of the Company owned by Gene E. Phillips or his affiliates in
excess of forty percent (40%) of the Company's outstanding shares shall be voted
in proportion to the votes cast by all non-affiliated shareholders of the
Company.

In accordance with the Olive Amendment, Richard W. Douglas, Larry E. Harley and
R. Douglas Leonhard were added to the Company's Board of Directors in January
1998 and Murray Shaw was added to the Company's Board of Directors in February
1998.



                     [THIS SPACE INTENTIONALLY LEFT BLANK.]

                                       12

<PAGE>   13



ITEM 6.        EXHIBITS AND REPORTS ON FORM 8-K


(a)   Exhibits:


Exhibit
Number                                Description
------                                -----------


 27.0          Financial Data Schedule, filed herewith.


(b)      Reports on Form 8-K as follows:

         A Current Report on Form 8-K, dated December 30, 1997, was filed
         January 9, 1998, with respect to Item 2. "Acquisition or Disposition of
         Assets," and Item 7. "Financial Statements and Exhibits," which reports
         the acquisition of Akard Plaza and Fireside Thrift Building, as amended
         by Form 8-K/A, filed August 5, 1998.

                                       13

<PAGE>   14





                                 SIGNATURE PAGE



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.



                                        INCOME OPPORTUNITY REALTY INVESTORS,
                                        INC.







Date:    August 5, 1998                 By:  /s/ Randall M. Paulson
     -----------------------               -------------------------------------
                                           Randall M. Paulson
                                           President






Date:    August 5, 1998                 By:  /s/ Thomas A. Holland
     -----------------------               -------------------------------------
                                           Thomas A. Holland
                                           Executive Vice President and
                                           Chief Financial Officer
                                           (Principal Financial and
                                           Accounting Officer)




                                       14

<PAGE>   15



                    INCOME OPPORTUNITY REALTY INVESTORS, INC.

                                   EXHIBITS TO
                          QUARTERLY REPORT ON FORM 10-Q

                    For the Three Months Ended June 30, 1998



<TABLE>
<CAPTION>
Exhibit                                                                      
Number                                  Description                            
------                                  -----------
 <S>                <C>
 27.0               Financial Data Schedule.                                 
</TABLE>