<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 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 number 0-2517


                          TOREADOR ROYALTY CORPORATION
             ------------------------------------------------------
             (Exact name of registrant as specified in its charter)


         Delaware                                         75-0991164
-------------------------------                        ---------------------
(State or other jurisdiction of                         (I.R.S. Employer
incorporation or organization)                        Identification Number)

     530 Preston Commons West
        8117 Preston Road
          Dallas, Texas                                          75225
---------------------------------------                        ----------
(Address of principal executive offices)                       (Zip Code)

Registrant's telephone number, including area code:  (214) 369-0080
                                                     --------------
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 twelve months, and (2) has been subject to such filing
requirements for the past 90 days.

                           Yes    X        No 
                                -----          ----

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

          Class                                  Outstanding at June 30, 1998
-------------------------------                  ----------------------------
Common Stock, $.15625 par value                      5,160,671 shares

<PAGE>   2

                          PART I. FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS

TOREADOR ROYALTY CORPORATION

CONSOLIDATED BALANCE SHEET

<TABLE>
<CAPTION>

                                                                       June 30,       December 31,
                                                                        1998             1997
                                                                     -----------      -----------
                                                                     (Unaudited)
ASSETS
Current assets:
<S>                                                                  <C>              <C>        
    Cash and cash equivalents                                        $ 3,315,971      $ 2,876,652
    Accounts receivable                                                  242,428          334,851
    Federal income tax receivable                                         60,588           62,307
    Deferred tax benefit                                                    --             15,945
    Other current assets                                                  39,485           26,956
                                                                     -----------      -----------

      Total current assets                                             3,658,472        3,316,711
                                                                     -----------      -----------

Properties and equipment, less accumulated
        depreciation, depletion and amortization                       3,538,425        3,210,074
                                                                     -----------      -----------

      Total assets                                                   $ 7,196,897      $ 6,526,785
                                                                     ===========      ===========

LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
    Accounts payable and accrued liabilities                         $   258,909      $   309,590

Deferred tax liabilities                                                  34,910             --
                                                                     -----------      -----------

      Total liabilities                                                  293,819          309,590
                                                                     -----------      -----------

Stockholders' equity:
    Preferred stock, $1.00 par value, 4,000,000
        shares authorized; none issued                                      --               --
    Common stock, $.15625 par value, 10,000,000
        shares authorized; 5,599,071 and 5,367,571 shares issued         874,855          838,683
    Capital in excess of par value                                     4,288,428        3,646,834
    Retained earnings                                                  2,894,484        2,791,117
                                                                     -----------      -----------
                                                                       8,057,767        7,276,634
    Treasury stock at cost:  438,400 shares and
        408,400 shares                                                (1,154,689)      (1,059,439)
                                                                     -----------      -----------

      Total stockholders' equity                                       6,903,078        6,217,195
                                                                     -----------      -----------

      Total liabilities and stockholders' equity                     $ 7,196,897      $ 6,526,785
                                                                     ===========      ===========
</TABLE>


          The Company uses the successful efforts method of accounting
                   for its oil and gas producing activities.
        See accompanying notes to the consolidated financial statements.

                                      -2-

<PAGE>   3
TOREADOR ROYALTY CORPORATION

CONSOLIDATED STATEMENT OF OPERATIONS
(UNAUDITED)

<TABLE>
<CAPTION>

                                                 For the Three Months Ended      For the Six Months Ended
                                                          June 30,                        June 30,
                                                 --------------------------      -------------------------
                                                    1998            1997            1998            1997
                                                 ----------      ----------      ----------     ----------
Revenues:
<S>                                                 <C>             <C>           <C>            <C>      
    Oil and gas sales                               454,943         449,702       1,090,688      1,127,537
    Lease bonuses and rentals                          --             2,800         168,664        112,738
    Interest and other income                        40,002          39,963          80,318         77,340
                                                 ----------      ----------      ----------     ----------

      Total revenues                                494,945         492,465       1,339,670      1,317,615

Costs and expenses:
    Lease operating expense                         139,244         141,930         307,957        280,145
    Dry holes and abandonments                       37,121          10,067         108,297         63,522
    Depreciation, depletion and amortization        114,971          56,754         207,746        114,342
    Geological and geophysical                       76,619          79,475         134,801        153,489
    General and administrative                      246,444         289,440         424,928        519,236
    Settlement of benefit plans                        --            86,317            --          115,488
                                                 ----------      ----------      ----------     ----------

      Total costs and expenses                      614,399         663,983       1,183,729      1,246,222
                                                 ----------      ----------      ----------     ----------

Income (loss) before federal income taxes          (119,454)       (171,518)        155,941         71,393

Provision (benefit) for federal income taxes        (40,668)        (55,189)         52,574         22,770
                                                 ----------      ----------      ----------     ----------

Net income (loss)                                   (78,786)       (116,329)        103,367         48,623
                                                 ==========      ==========      ==========     ==========

Basic income (loss) per share                         (0.02)          (0.02)           0.02           0.01
                                                 ==========      ==========      ==========     ==========

Diluted income (loss) per share                       (0.02)          (0.02)           0.02           0.01
                                                 ==========      ==========      ==========     ==========

Weighted average shares outstanding
Basic                                             5,115,546       5,098,093       5,052,652      5,069,684
Diluted                                           5,115,546       5,098,093       5,113,155      5,095,440
</TABLE>


        See accompanying notes to the consolidated financial statements.


                                      -3-
<PAGE>   4


TOREADOR ROYALTY CORPORATION

CONSOLIDATED STATEMENT OF CASH FLOWS
(UNAUDITED)
<TABLE>
<CAPTION>

                                                                         For the Three Months Ended       For the Six Months Ended
                                                                                  June 30,                       June 30,
                                                                        -----------     -----------      -----------    -----------
                                                                            1998           1997             1998             1997
                                                                        -----------     -----------      -----------    -----------
Cash flows from operating activities:
<S>                                                                     <C>             <C>              <C>            <C>        
    Net income (loss)                                                   $   (78,786)    $  (116,329)     $   103,367    $    48,623
    Adjustments to reconcile net income to
     net cash provided by operating activities:
      Depreciation, depletion and amortization                              114,971          56,754          207,746        114,342
      Dry holes and abandonments                                             37,121          10,067          108,297         63,522
      Decrease (increase)  in accounts receivable                            87,705          (3,757)          92,423        262,932
      Decrease (increase)  in federal income tax receivable                 (26,793)           --              1,719         54,899
      Decrease in pension obligation                                           --              --               --           87,208
      Decrease in other assets                                                 --            77,579             --             --
      Decrease (increase) in other current assets                           (18,047)         40,276          (12,529)        16,905
      Increase (decrease) in accounts payable and accrued liabilities        44,946          79,804          (50,681)      (147,266)
      Decrease (increase) in deferred tax benefit                              --           (61,671)          15,945        (62,938)
      Increase (decrease) in deferred tax expense                           (13,875)        (30,949)          34,910         (8,037)
                                                                        -----------     -----------      -----------    -----------

        Net cash provided by operating activities                           147,242          51,774          501,197        430,190
                                                                        -----------     -----------      -----------    -----------

Cash flows from investing activities:
     Expenditures for oil and gas property and equipment                   (304,534)        (53,940)        (644,394)      (149,697)
     Proceeds from lease bonuses and rentals                                   --              --               --           77,635
                                                                        -----------     -----------      -----------    -----------

        Net cash used by investing activities                              (304,534)        (53,940)        (644,394)       (72,062)
                                                                        -----------     -----------      -----------    -----------

Cash flows from financing activities:
    Sale of stock                                                           512,002            --            677,766           --
    Purchase of treasury stock                                                 --          (503,504)         (95,250)      (515,330)
                                                                        -----------     -----------      -----------    -----------

        Net cash provided (used) by financing activities                    512,002        (503,504)         582,516       (515,330)
                                                                        -----------     -----------      -----------    -----------


Net increase (decrease) in cash and cash equivalents                        354,710        (505,670)         439,319       (157,202)

Cash and cash equivalents, beginning of period                            2,961,261       3,422,579        2,876,652      3,074,111
                                                                        -----------     -----------      -----------    -----------

Cash and cash equivalents, end of period                                $ 3,315,971     $ 2,916,909      $ 3,315,971    $ 2,916,909
                                                                        ===========     ===========      ===========    ===========

Supplemental schedule of cash flow information:
     Cash received during the period for income taxes                   $      --       $      --        $      --      $    58,589
     Cash paid during period for income taxes                           $      --       $    40,000      $      --      $   100,000
</TABLE>


        See accompanying notes to the consolidated financial statements.

                                      -4-

<PAGE>   5


                          TOREADOR ROYALTY CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

                For the three and six months ended June 30, 1998

NOTE 1 - SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

         These consolidated financial statements should be read in the context
of the consolidated financial statements and notes thereto filed with the
Securities and Exchange Commission in the 1997 Annual Report on Form 10-K of
Toreador Royalty Corporation (the "Company"). In the opinion of the Company's
management, the information furnished herein reflects all adjustments consisting
of only normal recurring adjustments, necessary for a fair presentation of the
results of the interim periods reported herein. Operating results for the six
months ended June 30, 1998 may not necessarily be indicative of the results for
the year ending December 31, 1998. Certain previously reported financial
information has been reclassified to conform to the current period's
presentation.

NOTE 2 - NON-PRODUCING MINERAL AND ROYALTY INTERESTS

         Principal properties include mineral fee interests acquired by the
Company during 1951 and 1958. These interests total approximately 530,000 net
mineral acres underlying approximately 870,000 surface acres in the Texas
Panhandle and West Texas. It is recognized that the ultimate realization of the
investment in these properties is dependent upon future exploration and
development operations which are dependent upon satisfactory leasing and
drilling arrangements with others. Additionally, the Company owns working or
royalty interests in Texas, New Mexico, Oklahoma, Arkansas, Louisiana and
Colorado.

NOTE 3 - INTEREST AND OTHER INCOME

         Items in interest and other income consist of:
<TABLE>
<CAPTION>

                                    Three Months Ended                    Six Months Ended
                                         June 30,                             June 30,
                                -------------------------           ---------------------------
                                   1998            1997                1998             1997
                                ---------       ---------           ---------         ---------
<S>                             <C>             <C>                 <C>               <C>      
Interest                        $  39,387       $  39,963           $  76,613         $  76,196
Other Income                          615               -               3,705             1,144
                                ---------       ---------           ---------         ---------

                                $  40,002       $  39,963           $  80,318         $  77,340
                                =========       =========           =========         =========
</TABLE>


NOTE 4 - COMPREHENSIVE INCOME

         Effective January 1, 1998, the Company adopted Statement of Financial
Accounting Standard No. 130, "Reporting Comprehensive Income." The adoption of
this Statement had no effect on the Company's financial statements.


                                      -5-
<PAGE>   6


                          TOREADOR ROYALTY CORPORATION

                For the three and six months ended June 30, 1998

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

         DISCLOSURES REGARDING FORWARD-LOOKING STATEMENTS

         This report on Form 10-Q includes "forward-looking statements" within
the meaning of Section 27A of the Securities Act of 1933, as amended, and
Section 21E of the Securities Exchange Act of 1934, as amended. All statements
other than statements of historical facts included in this Form 10-Q, including,
without limitation, statements contained in this "Management's Discussion and
Analysis of Financial Condition and Results of Operations" regarding the
Company's financial position, business strategy, plans and objectives of
management of the Company for future operations, and industry conditions, are
forward-looking statements. Although the Company believes that the expectations
reflected in such forward-looking statements are reasonable, it can give no
assurance that such expectations will prove to be correct. Any forward-looking
statements herein are subject to certain risks and uncertainties inherent in
petroleum exploration, development and production, including, but not limited to
the risk that no commercially productive oil and gas reservoirs will be
encountered; inconclusive results from 3-D seismic projects; delays or
cancellation of drilling operations as a result of a variety of factors;
volatility of oil and gas prices due to economic and other conditions; intense
competition in the oil and gas industry; operational risks (e.g., fires,
explosions, blowouts, cratering and loss of production); insurance coverage
limitations and requirements; and potential liability imposed by intense
governmental regulation of oil and gas production; all of which are beyond the
control of the Company. Any one or more of these factors could cause actual
results to differ materially from those expressed in any forward-looking
statement. All subsequent written and oral forward-looking statements
attributable to the Company or persons acting on its behalf are expressly
qualified in their entirety by the cautionary statements disclosed in this
paragraph and otherwise in this report.

         LIQUIDITY AND CAPITAL RESOURCES

         Historically, most of the exploration activity on the Company's acreage
has been funded and conducted by other oil companies. Exploration activity by
third party oil companies typically generates lease bonus and option income to
the Company. If such drilling is successful, the Company receives royalty income
from the oil or gas production but bears none of the capital or operating costs.

         In order to accelerate the evaluation of its acreage as well as
increase its ownership in any reserves that are discovered, the Company has
increased and intends to further increase its level of participation in
exploring its acreage by acquiring working interests. The extent to which the
Company may acquire working interests will depend on the availability of outside
capital and cash flow from operations.

         Currently, the primary source of capital for financing the Company's
operations is its cash flow from operations. On November 13, 1997, the Company
obtained a $10 million


                                      -6-
<PAGE>   7


                          TOREADOR ROYALTY CORPORATION

                For the three and six months ended June 30, 1998

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

credit facility from Compass Bank. This credit facility has a current borrowing
base limitation of $4 million which the Company may use to fund acquisition and
development of oil and gas properties. To date, the Company has not drawn any
amounts under the facility.

         Under the terms of this credit facility, the interest rate is dependent
on the Principal Debt then outstanding. For Principal Debt equal to or less than
80% of the Borrowing Base then in effect, the unpaid principal balance of the
Note is subject to a fluctuating interest rate (per annum) equal to the
fluctuating CBIR Rate (or prime) less 0.5%. For Principal Debt greater than 80%
of the Borrowing Base then in effect, the unpaid principal balance of the Note
is subject to a fluctuating interest rate (per annum) equal to the fluctuating
CBIR Rate. Unpaid balances are paid quarterly commencing January 1, 1998.
Borrowings up to $2 million are unsecured. The credit facility contains a Letter
of Credit subfeature which imposes a fee of 0.875% per annum on the face amount
of the Letter of Credit, with a minimum of $350. The Company is subject to an
Unused Commitment Fee computed at the rate of 0.375% per annum on the average
daily unused portion of the commitment. Such fee is payable quarterly in arrears
beginning January 1, 1998.

         The credit facility contains various affirmative and negative
covenants. These covenants, among other things, limit additional indebtedness,
the sale of assets and the payment of dividends, change of control and
management and require the Company to meet certain financial tests.

         The Company has from time to time and may continue to reinvest proceeds
from option and lease bonuses by taking a working interest in selected 3-D
seismic projects or wells. To the extent cash flow from operations does not
significantly increase and external sources of capital are limited or
unavailable (including those funds made available pursuant to the terms of the
credit facility), the Company's ability to make the capital investment to
participate in 3-D seismic surveys and increase its interest in projects on its
acreage will be limited. Future funds are expected to be provided through
production from existing producing properties and new producing properties that
may be discovered through exploration of the Company's acreage by third parties
or by the Company itself. Funds could also be provided through external
financing in the form of debt or equity, although there are no current plans to
do so. There can be no assurance as to the extent and availability of these
sources of funding.

         As of the date of this report, the Company is not aware of any demands,
commitments or events which will result in its liquidity increasing or
decreasing in a material way. The Company presently has no debt and maintains
its excess cash funds in interest-bearing deposits. From time to time, the
Company may receive lease bonuses that cannot be anticipated and, when funds are
available, the Company may elect to participate in exploratory ventures. The
Company also may acquire producing oil and gas assets


                                      -7-
<PAGE>   8


                          TOREADOR ROYALTY CORPORATION

                For the three and six months ended June 30, 1998

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

which could require the use of debt including the aforementioned credit facility
or other forms of financing.

         Management believes that sufficient funds are available from internal
sources and its available credit facility to meet anticipated capital
requirements for fiscal 1998.

         In September 1997, the Company engaged Dain Rauscher Wessels (formerly
Rauscher Pierce Refsnes, Inc.) as its financial advisor in evaluating strategic
alternatives available to the Company, including a sale of the Company, a merger
with another company and other forms of business combinations. Since that time,
the Company has concluded that for the foreseeable future the optimum means of
increasing stockholder value is to continue with its efforts to generate
exploration activity on its mineral acreage and to increase exploration activity
through acquisition of interests in oil and gas properties.

         The Company has used $1,137,946 of its cash reserves to purchase
432,700 shares of its Common Stock, as of June 30, 1998. These purchases were
made pursuant to stock repurchase programs authorized by the Board of Directors
on October 10, 1995, of up to 100,000 shares of Common Stock, a second stock
repurchase program on April 22, 1996, of up to 150,000 shares of common stock
and a third stock repurchase program on April 21, 1997, of up to 300,000 shares
of common stock. As of August 11, 1998, the Company had purchased an aggregate
of 182,700 shares at a purchase price of $506,918 under the third repurchase
program. The repurchases of the Company's shares of Common Stock were made in
unsolicited open-market purchases, at market (not premium) prices, without fixed
terms and not contingent upon the tender of a fixed minimum number of shares or
in response to a third party bid and otherwise in accordance with Rule 10b-18
under the Securities Exchange Act of 1934, as amended.

         During the first six months of 1998, the Company received a total of
$677,766 as a result of the exercise of stock options to purchase the Company's
Common Stock by two former employees. Those options related to 200,000 and
31,500 shares with exercise prices of $3.00 and $2.46875 per share,
respectively. As of June 15, 1998, neither of the two former employees held the
right to exercise options for additional shares of the Company's Common Stock.
Funds received from the exercise of these stock options were added to the
Company's working capital and used for general corporate purposes.


                                      -8-
<PAGE>   9



                          TOREADOR ROYALTY CORPORATION

                For the three and six months ended June 30, 1998

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

RESULTS OF OPERATIONS

   THREE MONTHS ENDED JUNE 30, 1998 VS.
      THREE MONTHS ENDED JUNE 30, 1997

         Revenues for the second quarter of 1998 were $494,945 versus $492,465
for the same period in 1997. Oil and gas sales were $454,943 on volumes of
28,004 Bbls of oil and 51,779 Mcf of natural gas as compared to $449,702 on
volumes of 19,233 Bbls and 80,569 Mcf in 1997. This 1.2% increase in oil and gas
sales reflects the impact of lower oil prices despite the higher oil volumes
coupled with lower gas volumes in spite of higher gas prices. The average price
for second quarter 1998 oil sales decreased 24.6% to $13.20/Bbl compared to
$17.50/Bbl for the same quarter in 1997. The average price for second quarter
1998 gas sales increased 15.9% to $1.68/Mcf compared to $1.45/Mcf for the same
period in 1997. There were no lease bonuses and rentals for the second quarter
of 1998 versus $2,800 for the same period in 1997. Interest and other income was
$40,002 in the second quarter of 1998 versus $39,963 for the second quarter of
1997.

         Costs and expenses for the second quarter of 1998 were $614,399 in 1998
versus $663,983 for the same period in 1997. Lease operating expenses decreased
slightly to $139,244 in 1998 from $141,930 in 1997. Dry holes and abandonments
increased to $37,121 in 1998 from $10,067 in 1997 primarily reflecting increased
participation in exploration projects on the Company's mineral acreage versus a
year ago. Depreciation, depletion and amortization increased 102.6% to $114,971
in 1998 from $56,754 in 1997, primarily reflecting downward reserve adjustments
made at year ended December 31, 1997. Geological and geophysical expenses
decreased 3.6% to $76,619 in 1998 from $79,475 in 1997. General and
administrative expenses decreased 14.9% to $246,444 from $289,440 a year ago
primarily reflecting a decrease in salaries.

         The Company recognized a net loss of $78,786, or $0.02 per share
(basic), for the second quarter of 1998 versus a net loss of $116,329, or $0.02
per share (basic), for the same period in 1997.


                                      -9-
<PAGE>   10


                          TOREADOR ROYALTY CORPORATION

                For the three and six months ended June 30, 1998

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

RESULTS OF OPERATIONS

   SIX MONTHS ENDED JUNE 30, 1998 VS.
      SIX MONTHS ENDED JUNE 30, 1997

         Revenues for the six months ended June 30, 1998 were $1,339,670 versus
$1,317,615 for the same period in 1997. Oil and gas sales for the six months
ended June 30, 1998 were $1,090,688 on volumes of 47,981 Bbls of oil and 199,435
Mcf of natural gas as compared to $1,127,537 on volumes of 37,092 Bbls and
159,892 Mcf for the same period in 1997. The $36,849 decrease in oil and gas
sales reflects the impact of lower oil and gas prices which offset the increase
in oil and gas volumes. Average oil prices decreased 29.7% to $14.09/Bbl for the
six months ended June 30, 1998 from $20.05/Bbl for the six months ended June 30,
1997. Average gas prices decreased 13.6% to $2.09/Mcf for the six months ended
June 30, 1998 from $2.42/Mcf for the six months ended June 30, 1997. Lease
bonuses and rentals increased to $168,664 for the six months ended June 30, 1998
compared to $112,738 for the prior-year six month period. This 49.6% increase
was primarily attributable to a lease bonus and seismic reimbursement on
additional acreage taken on the Company's mineral acreage. Interest and other
income for the six months ended June 30, 1998 was $80,318 in 1998, up slightly
from $77,340 for the same period in 1997.

         Costs and expenses for the six months ended were $1,183,729 in 1998
versus $1,246,222 for the same period in 1997. Lease operating expenses
increased to $307,957 for the six months ended June 30, 1998 from $280,145 for
the same period in 1997 primarily due to the exploration success the Company had
on it minerals in the fourth quarter of 1997, and in part, the first quarter of
1998. Dry holes and abandonments increased to $108,297 for the six period ended
June 30, 1998 from $63,522 for the six months ended June 30, 1997 reflecting the
Company's increased participation in exploration projects on its minerals, most
of which occurred in the first quarter of 1998. Depreciation, depletion and
amortization increased 81.7% to $207,746 for the first six months in 1998 from
$114,342 for the same period in 1997, reflecting more property owned by the
Company and downward reserve adjustments made at year ended December 31, 1997.
Geological and geophysical expenses decreased 12.2% to $134,801 for the six
months ended June 30, 1998 from $153,489 for the prior-year period. General and
administrative expenses decreased to $424,928 for the six months ended June 30,
1998 from $519,236 for the same period a year ago, primarily due to a reduction
in salaries.

         The Company recognized net income of $103,367 or $0.02 per share
(basic), for the six months ended June 30, 1998 versus net income of $48,623, or
$0.01 per share (basic), for the same period in 1997.


                                      -10-
<PAGE>   11



                          TOREADOR ROYALTY CORPORATION

                For the three and six months ended June 30, 1998

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

NEW ACCOUNTING PRONOUNCEMENTS

         In June 1998, the Financial Accounting Standards Board issued Statement
of Financial Accounting Standards No. 133, "Accounting for Derivative
Instruments and Hedging Activities." This statement requires companies to record
derivatives on the balance sheet as assets and liabilities, measured at fair
value. Gains and losses resulting from changes in the values of those
derivatives would be accounted for depending on the use of the derivative and
whether it qualifies for hedge accounting. This statement is not expected to
have a material impact on the Company's consolidated financial statements. This
statement is effective for all fiscal quarters of all fiscal years beginning
after June 15, 1999, with earlier adoption encouraged.

YEAR 2000 ISSUE

         The Company has completed the initial assessment of its computer
systems and other operational equipment to determine what systems and equipment
may be impacted by the Year 2000 problem. The Company presently believes that it
will be able to implement successfully the required systems and equipment
modifications necessary to make the Company Year 2000 compliant by mid-1999.
Based on the Company's assessment of its computer systems and other operational
equipment to date, the Company believes that the potential impact, if any, of it
not timely implementing the necessary modifications to become Year 2000
compliant would not be material to the operations of the Company. The Company
currently estimates that the costs that will be incurred to become Year 2000
compliant will not be material to the Company.

         The Company has initiated formal communication with its significant
suppliers and business partners to determine the extent to which the Company is
vulnerable to these third parties' failure to remedy their own Year 2000 issues.
In addition, third party vendors of hardware and packaged software have been
contacted about their products' compliance status. There can be no assurance
that the systems of other companies on which the Company's systems rely will be
timely converted, or that a failure to convert by another company, or a
conversion that is incompatible with the Company's systems, would not have a
material adverse effect on the Company, all of which is beyond the control of
the Company.


                                      -11-
<PAGE>   12



                          TOREADOR ROYALTY CORPORATION

                                  June 30, 1998

                           PART II. OTHER INFORMATION

ITEM 1.   LEGAL PROCEEDINGS -- Inapplicable.

ITEM 2.   CHANGES IN SECURITIES

         See ITEM 5 below for a description of certain amendments to the
Company's stockholders rights plan.

ITEM 3.   DEFAULTS UPON SENIOR SECURITIES -- Inapplicable.

ITEM 4.   SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

         (a) The annual meeting of stockholders of the Company was held at 10:00
a.m., local time, on Thursday, July 23, 1998.

         (b) Proxies were solicited by the Board of Directors of the Company
pursuant to Regulation 14A under the Securities Exchange Act of 1934. There was
no solicitation in opposition to the Board of Directors' nominees as listed in
the proxy statement and all of such nominees were duly elected.

         (c) Out of a total of 5,146,771 shares of common stock of the Company
outstanding and entitled to vote, 4,240,831 shares were present in person or by
proxy, representing approximately 82 percent. The only matter voted on by the
stockholders, as fully described in the definitive proxy materials for the
annual meeting, was the election of directors of the Company. The results of the
voting for the election of directors of the Company were as follows:


<TABLE>
<CAPTION>

                                                                                  Number of Shares
                                                                                     WITHHOLDING
                                               Number of Shares Voting          AUTHORITY to Vote for
               Nominees                       FOR Election as Director          Election as Director
               --------                       ------------------------          --------------------
<S>                                                   <C>                               <C>  
            J. W. Bullion                             4,235,799                         5,032
          Edward Nathan Dane                          4,177,654                        63,177
            Peter L. Falb                             4,177,654                        63,177
         G. Thomas Graves III                         4,230,299                        10,532
        Thomas P. Kellogg, Jr.                        4,235,999                         4,832
            William I. Lee                            4,231,499                         9,332
         John Mark McLaughlin                         4,236,999                         3,832
</TABLE>

There were no broker non-votes for the election of directors voted on by the
stockholders at the annual meeting.

         (d)      Inapplicable.


                                      -12-
<PAGE>   13


                          TOREADOR ROYALTY CORPORATION

                                  June 30, 1998

                           PART II. OTHER INFORMATION

ITEM 5.   OTHER INFORMATION

         On June 29, 1998, the Company announced that G. Thomas Graves III was
elected president and chief executive officer, effective at the conclusion of
the Company's annual stockholder meeting which was held on July 23, 1998. Other
changes included four new board candidates nominated for election to replace
three prior directors who were not nominated for re-election by the board of
directors. Also, it was announced that the Company's board of directors amended
the Company's stockholders rights plan to reflect additional circumstances under
which the plan would not be triggered, as detailed in the Form 8-K specified
under ITEM 6, which is incorporated by reference herein.

ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K.

         (a)   Exhibits

         The information required by this Item 6(a) is set forth in the Index to
Exhibits accompanying this quarterly report and is incorporated herein by
reference.

         (b)   Reports on Form 8-K

         Form 8-K dated July 1, 1998 (Date of Event: June 25, 1998), which
reported that certain stockholders and certain members of the Board of Directors
acting in their capacity as stockholders of the Company entered into three
separate agreements, namely, a Stockholder Voting Agreement, a Settlement
Agreement between the parties therein and an amendment to the Rights Agreement.
No financial statements were filed with this Form 8-K.

                                   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.

                                          TOREADOR ROYALTY CORPORATION,
                                                   Registrant

                                            /s/ G. Thomas Graves III
                                          ------------------------------------
                                                G. Thomas Graves III,
                                          President and Chief Executive Officer

August 11, 1998

                                      -13-
<PAGE>   14


                          TOREADOR ROYALTY CORPORATION

                                  June 30, 1998

                                INDEX TO EXHIBITS


      Exhibit
      Number                           Exhibits
   --------------     ---------------------------------------------------------

        27        -   Financial Data Schedule