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

                                    FORM 10-Q

Mark One
     X          QUARTERLY REPORT UNDER SECTION 13 OR 15 (d)
    ---         OF THE SECURITIES AND EXCHANGE ACT OF 1934

For the quarterly period ended June 30, 1998.

                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 1-2677

                            QUAKER STATE CORPORATION
             (Exact name of registrant as specified in its charter)

                Delaware                                     25-0742820
     (State or other jurisdiction of                       (IRS Employer
     incorporation of organization)                      Identification No.)



                         225 East John Carpenter Freeway
                               Irving, Texas 75062
                    (Address of Principal Executive Offices)
                                   (Zip Code)

                                  (972)868-0400
              (Registrant's telephone number, including area code)

                                 Not applicable
              (Former name, former address and former fiscal year,
                          if changed since last report)

         Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months and (2) has been subject to such filing
requirements for the past 90 days.

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

         As of July 31, 1998, 36,384,301 shares of Capital Stock, par value
$1.00 per share, of the registrant were outstanding.


<PAGE>   2

PART I.  FINANCIAL INFORMATION
Item 1.  Financial Statements

QUAKER STATE CORPORATION AND SUBSIDIARIES
Condensed Consolidated Statement of Income

<TABLE>
<CAPTION>
                                                               Quarter Ended                  Six Months Ended
(in thousands except per share data, unaudited)           6/30/98         6/30/97         6/30/98          6/30/97
====================================================================================================================
<S>                                                    <C>              <C>             <C>              <C>
REVENUES
Sales and operating revenues                           $   312,879      $   319,274     $   611,408      $   613,627
Other, net                                                     951            1,362           2,580            3,419
                                                       -------------------------------------------------------------
                                                           313,830          320,636         613,988          617,046
                                                       -------------------------------------------------------------
COSTS AND EXPENSES
Cost of sales and operating costs                          184,629          203,841         368,496          395,601
Selling, general and administrative                         91,620           87,004         180,331          165,842
Depreciation and amortization                               11,427           10,212          22,780           19,953
Interest                                                     7,555            6,737          14,514           13,062
Systems integration, merger and
    restructuring charges                                   15,249             --            21,674             --
                                                       -------------------------------------------------------------
                                                           310,480          307,794         607,795          594,458
                                                       -------------------------------------------------------------
Income from continuing operations before
    income taxes                                             3,350           12,842           6,193           22,588
Provision for income taxes                                   1,575            5,275           2,800            9,250
                                                       -------------------------------------------------------------
Income from continuing operations                            1,775            7,567           3,393           13,338
Income from discontinued operations                           --              1,277            --              2,371
                                                       -------------------------------------------------------------
NET INCOME                                             $     1,775      $     8,844     $     3,393      $    15,709
====================================================================================================================

PER SHARE (BASIC AND DILUTED)
Income from continuing operations                      $       .05      $       .21     $       .09      $       .38
Income from discontinued operations                           --                .04            --                .07
                                                       -------------------------------------------------------------
NET INCOME                                             $       .05      $       .25     $       .09      $       .45
====================================================================================================================

Weighted average shares outstanding - Basic                 36,421           35,104          36,361           34,992
Weighted average shares outstanding - Diluted               37,236           35,330          36,907           35,156
====================================================================================================================

Dividends paid per share                               $       .10      $       .10     $       .20      $       .20
====================================================================================================================

COMPREHENSIVE INCOME
Net income                                             $     1,775      $     8,844     $     3,393      $    15,709
Foreign currency translation adjustment,
    net of tax                                                (240)             115            (343)              82
                                                       -------------------------------------------------------------
Comprehensive income                                   $     1,535      $     8,959     $     3,050      $    15,791
====================================================================================================================
</TABLE>

The accompanying notes are an integral part of the financial statements.


                                       2
<PAGE>   3

QUAKER STATE CORPORATION AND SUBSIDIARIES
Condensed Consolidated Statement of Cash Flows

<TABLE>
<CAPTION>
SIX MONTHS ENDED JUNE 30
(in thousands, unaudited)                                                1998                1997
======================================================================================================
<S>                                                                 <C>                  <C>
NET CASH USED IN OPERATING ACTIVITIES                               $    (23,325)        $     (6,134)
                                                                    ---------------------------------
CASH FLOW FROM INVESTING ACTIVITIES
Capital expenditures                                                     (19,431)             (25,965)
Proceeds from disposal of property and equipment                           3,589                1,378
Acquisition of businesses, net of cash acquired                           (7,449)             (21,213)
Taxes paid on sale of discontinued operations                            (12,250)                --
Other, net                                                                 5,327               (7,822)
                                                                    ---------------------------------
     Net cash used in investing activities                               (30,214)             (53,622)
                                                                    ---------------------------------
CASH FLOW FROM FINANCING ACTIVITIES
Dividends paid                                                            (7,270)              (6,980)
Proceeds from debt                                                        59,130              212,999
Payments on debt                                                          (6,700)            (166,603)
Other, net                                                                 1,679                 --
                                                                    ---------------------------------
     Net cash provided by financing activities                            46,839               39,416
                                                                    ---------------------------------
Net decrease in cash and cash equivalents                                 (6,700)             (20,340)
Total cash and cash equivalents at beginning of period                    20,205               29,397
                                                                    ---------------------------------
TOTAL CASH AND CASH EQUIVALENTS AT END OF PERIOD                    $     13,505         $      9,057
=====================================================================================================
</TABLE>

The accompanying notes are an integral part of the financial statements.


                                       3
<PAGE>   4

QUAKER STATE CORPORATION AND SUBSIDIARIES
Condensed Consolidated Balance Sheet

<TABLE>
<CAPTION>
                                                                            June 30,      December 31,
(in thousands, except share data)                                            1997            1998
=====================================================================================================
                                                                          (unaudited)
<S>                                                                      <C>             <C>
ASSETS
Current assets:
Cash and cash equivalents                                                $     13,505    $     20,205
Accounts and notes receivable, less allowance of $5,416 and
     $4,696 in 1998 and 1997                                                  216,068         186,654
Inventories                                                                    91,117          90,821
Other current assets                                                           20,283          20,068
                                                                         ----------------------------
   Total current assets                                                       340,973         317,748
                                                                         ----------------------------
Property, plant and equipment, at cost                                        251,820         247,073
Goodwill, brands and other assets                                             602,702         604,894
                                                                         ----------------------------
     TOTAL ASSETS                                                        $  1,195,495    $  1,169,715
=====================================================================================================

LIABILITIES
Current liabilities:
Accounts payable                                                         $     71,280    $     70,805
Accrued liabilities                                                           109,608         130,088
Debt payable within one year                                                    5,157          11,477
                                                                         ----------------------------
   Total current liabilities                                                  186,045         212,370
                                                                         ----------------------------
Long-term debt                                                                487,948         429,198
Other long-term liabilities                                                   190,682         196,246
                                                                         ----------------------------
   Total liabilities                                                          864,675         837,814
                                                                         ----------------------------
Commitments and contingencies

STOCKHOLDERS' EQUITY
Capital stock $1.00 par value; authorized shares, 250,000,000;
   issued shares, 38,154,591 and 37,977,144 in 1998 and 1997                   38,155          37,977
Additional capital                                                            213,250         210,734
Retained earnings                                                             108,574         112,451
Cumulative foreign currency translation adjustment                               (210)            133
Treasury stock, at cost, 1,723,772 and 1,699,593 in 1998 and 1997             (27,401)        (26,924)
Unearned compensation                                                          (1,548)         (2,470)
                                                                         ----------------------------
   Total stockholders' equity                                                 330,820         331,901
                                                                         ----------------------------
     TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                          $  1,195,495    $  1,169,715
=====================================================================================================
</TABLE>

The accompanying notes are an integral part of the financial statements.


                                       4
<PAGE>   5

QUAKER STATE CORPORATION AND SUBSIDIARIES
Segment Information

<TABLE>
<CAPTION>
                                                         Quarter Ended                    Six Months Ended
(in thousands, unaudited)                            6/30/98         6/30/97          6/30/98          6/30/97
================================================================================================================
<S>                                               <C>              <C>               <C>              <C>
REVENUES
Lubricants and lubricant services                 $   220,004      $   244,744      $   433,675      $   469,283
Consumer products                                      95,379           77,795          182,347          149,270
Intersegment sales                                     (2,504)          (3,265)          (4,614)          (4,926)
                                                  --------------------------------------------------------------
Total operating revenues                          $   312,879      $   319,274      $   611,408      $   613,627
================================================================================================================
OPERATING PROFITS
Lubricants and lubricant services                 $    16,130      $    12,602      $    25,888      $    21,270
Systems integration, merger and
    restructuring charges                              (3,588)            --             (6,440)            --
                                                  --------------------------------------------------------------
Total lubricants and lubricant services                12,542           12,602           19,448           21,270
                                                  --------------------------------------------------------------
Consumer products                                      14,933           12,694           26,342           24,885
Systems integration, merger and
    restructuring charges                              (3,588)            --             (6,440)            --
                                                  --------------------------------------------------------------
Total consumer products                                11,345           12,694           19,902           24,885
                                                  --------------------------------------------------------------
Total operating profits                                23,887           25,296           39,350           46,155
Interest expense                                       (7,555)          (6,737)         (14,514)         (13,062)
Corporate other income                                    123              191              264              381
Corporate expense                                      (5,032)          (5,908)         (10,113)         (10,886)
Systems integration, merger and
    restructuring charges                              (8,073)            --             (8,794)            --
                                                  --------------------------------------------------------------
Total corporate expenses                              (13,105)          (5,908)         (18,907)         (10,886)
                                                  --------------------------------------------------------------
Income from continuing operations before
    income taxes                                  $     3,350      $    12,842      $     6,193      $    22,588
================================================================================================================
</TABLE>

The accompanying notes are an integral part of the financial statements.


                                       5
<PAGE>   6

NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
Quaker State Corporation and Subsidiaries (unaudited)

1.   In the opinion of management of Quaker State Corporation (the "Company"),
     the accompanying financial statements include all adjustments which are
     necessary for a fair statement of the results for such periods. All of
     these adjustments are of a normal recurring nature. The December 31, 1997
     condensed consolidated balance sheet was derived from audited financial
     statements, but does not include all disclosures required by generally
     accepted accounting principles. These statements should be read in
     conjunction with the financial statements included in the 1997 Annual
     Report on Form 10-K.

2.   Special charges of $21.7 million in the first six months of 1998 are
     comprised of $11.7 million of systems integration costs, $8.8 million of
     merger costs (see Note 8) and $1.2 million of restructuring costs.

3.   The effective tax rates are higher than the 35% federal statutory rate due
     to the impact of state and foreign taxes and nondeductible amortization.

4.   The difference between basic and diluted weighted average shares of capital
     stock outstanding for the quarter and six months ended June 30, 1998 and
     1997 is due to dilutive stock options of 815,000 and 546,000, and 226,000
     and 164,000, respectively.

5.   The following schedule is prepared on a pro forma basis as though the
     assets of Auto-Shade, L.L.C. and Auto-Shade (Overseas) L.L.C. ("Axius") and
     Rain-X Corporation ("Rain-X") had been acquired as of January 1, 1997 and
     Truck-Lite Co. Inc. ("Truck-Lite") was sold as of January 1, 1997, after
     including the impact of adjustments, such as amortization of goodwill,
     brands and other intangible assets, interest expense and related tax
     effects.

<TABLE>
<CAPTION>
       For the six months ended June 30, 1997 (in thousands except per share data)
       ---------------------------------------------------------------------------
       <S>                                                             <C>
       Revenues                                                        $   650,444
       Income from continuing operations                                    14,674
       Income per share from continuing operations                             .41
       ===========================================================================
</TABLE>

     The pro forma results are not necessarily indicative of what would have
     occurred if the acquisitions had been in effect for the period presented.
     In addition, they are not intended to be a projection of future results.

6.   Inventories are stated at the lower of cost or market. Cost is determined
     on the last-in, first-out ("LIFO") basis for manufactured products. For
     other inventories, such as purchased finished lubricating oils and
     purchased automotive aftermarket products, cost is determined on the
     first-in, first-out ("FIFO") basis. The reserve to reduce the carrying
     value of inventories from FIFO basis to LIFO basis amounted to $ 5.7
     million at June 30, 1998 and $7.5 million at December 31, 1997. Inventories
     consist of:

<TABLE>
<CAPTION>
                                                         June 30,      December 31,
       (in thousands)                                      1998           1997
       ---------------------------------------------------------------------------
       <S>                                             <C>            <C>
       Lubricants and related materials                $     56,331   $     59,242
       Consumer products                                     34,786         31,579
                                                       ------------   ------------
       Total                                           $     91,117   $     90,821
       ===========================================================================
</TABLE>

     Certain inventory quantities were reduced resulting in liquidation of LIFO
     inventory which increased net income by $780,000 or $.02 per share for the
     six months ended June 30, 1998.


                                       6
<PAGE>   7

NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS, CONTINUED

7.     In 1996, the Federal Trade Commission ("FTC") filed an administrative
       proceeding seeking an order that Slick 50 cease from making certain
       product claims and refrain from making other product claims without
       adequate substantiation. In addition, class action suits were filed
       against Slick 50 alleging false, misleading, deceptive and/or
       unsubstantiated claims relating to Slick 50(R)engine treatment. In
       December 1997, the FTC approved and entered a consent decree settling the
       administrative proceeding. The consent decree includes restrictions on
       the future advertising of Slick 50(R)products and an agreement by the FTC
       not to seek consumer redress provided Slick 50 makes available at least
       $10 million in consumer redress in the form of coupons, refunds or free
       products for former purchasers of Slick 50 products. The Company also
       reached a settlement with counsel in all of the class actions except one,
       under which the Company will make available to class members $20 million
       in cash rebates usable against future purchases of a variety of the
       products or services of the Company and its subsidiaries and to pay
       attorneys' fees to counsel for the class of $3.25 million. The Company
       will also pay all costs of notice and settlement administration. The
       District Court for Dallas County, Texas, entered an order approving the
       settlement on July 14, 1998. The settlement of the class action suits
       will fulfill the consumer redress requirements under the FTC consent
       decree.

       On July 28, 1998, Oil Changer, Inc. ("Oil Changer") and several
       corporations affiliated with Oil Changer filed a suit in the Superior
       Court of the State of California, Alameda County, against the Company,
       certain executives of the Company and other individuals. The complaint
       alleges that the Company and Oil Changer were "strategic partners" in an
       alleged partnership to develop quick lubrication centers in Northern
       California. Oil Changer alleges that the Company breached the alleged
       agreement by developing quick lubrication centers with another entity.
       The complaint asserts claims for fraud, breach of fiduciary duty and
       usurpation of partnership opportunity, partnership accounting, breach of 
       contract, conspiracy and violation of Section 17200 of the California
       Business Professions Code. Plaintiffs seek compensatory damages of $50
       million, punitive damages, restitution, attorneys' fees and costs as well
       as injunctive relief.

       In addition, on July 28, 1998, Oil Changer and several corporations
       affiliated with Oil Changer filed a complaint in the United States
       District Court for the Northern District of California against the
       Company and Pennzoil Company ("Pennzoil"). The complaint asserts claims
       under Sections 1 and 2 of the Sherman Act, Section 7 of the Clayton Act
       and Sections 16720 and 17200 of the California Business Professions Code,
       alleging that the proposed merger of the Company and Pennzoil's
       downstream business (see Note 8) will substantially lessen competition
       in, or result in monopolization of, the markets for motor oil and quick
       lubrication services in certain areas of California. Plaintiffs seek
       compensatory and treble damages, restitution, attorneys' fees and costs
       as well as injunctive relief enjoining the proposed merger.

       The Company has received notices from the EPA and others that it is a
       "potentially responsible party" relative to certain waste disposal sites
       identified by the EPA and may be required to share in the cost of
       cleanup. The Company has accrued for all matters, which are probable and
       can be reasonably estimated.

       Contingent liabilities of an indeterminate amount exist in connection
       with suits and claims arising in the ordinary course of business.

       In the opinion of management, all matters discussed above are adequately
       accrued for or covered by insurance, or, if not so provided for, are
       without merit or the disposition is not anticipated to have a material
       effect on the Company's financial position; however, one or more of these
       matters could have a material effect on future quarterly or annual
       results of operations or cash flow when resolved.


                                       7
<PAGE>   8

NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS, CONTINUED

8.     On April 14, 1998, the Company, Pennzoil and certain Pennzoil
       subsidiaries entered into an Agreement and Plan of Merger (the "Merger
       Agreement"). The Merger Agreement and related agreements provide for the
       separation of Pennzoil's motor oil, refined products and franchise
       operations from its exploration and production operations and for the
       combination of the motor oil, refined products and franchise operations
       with the Company. Closing under the Merger Agreement is conditioned on,
       among other things, approval by the Company's stockholders, expiration or
       termination of waiting periods under the Hart-Scott-Rodino Antitrust
       Improvements Act of 1976 ("HSR Act"), and receipt of a favorable tax
       ruling from the Internal Revenue Service. The waiting period under the
       HSR Act expired on May 27, 1998.

       The Merger Agreement, if consummated, would result in a Change of Control
       (as defined in the Company's $400 million Credit Agreement). Under the
       terms of the Credit Agreement, the Company would be required to notify
       each Bank (as defined in the Credit Agreement) that a Change of Control
       has occurred within ten days of such occurrence, and each Bank may
       terminate its Commitment (as defined in the Credit Agreement) and declare
       the Note (as defined in the Company's Credit Agreement) immediately due
       and payable with three Domestic Business Days (as defined in the Credit
       Agreement) notice given not later than sixty days after such Change of
       Control.

9.     In June 1998, the Financial Accounting Standards Board issued Standard
       No. 133 "Accounting for Derivative Instruments and Hedging Activities."
       The Standard establishes accounting and reporting standards for
       derivative instruments, including certain derivative instruments embedded
       in other contracts, (collectively referred to as derivatives) and for
       hedging activities. The new Standard is effective for all fiscal quarters
       of all fiscal years beginning after June 15, 1999. The Company does not
       expect the adoption of the new Standard to have a material impact on its
       financial position or results of operations.


Item 2. Management's Discussion and Analysis of Results of Operations and
        Financial Condition

The condensed consolidated financial statements, segment information and related
notes for Quaker State Corporation (the "Company") included in this Form 10-Q,
should be read as an integral part of this analysis.

The Company reported net income of $1.8 million or $.05 per share for the
quarter ended June 30, 1998, compared to net income of $8.8 million or $.25 per
share for the quarter ended June 30, 1997. The second quarter 1998 net income
includes charges of $9.2 million (after-tax) relating to systems integration,
merger and restructuring. The second quarter 1997 net income includes $1.3
million of income from the Company's discontinued Truck-Lite operations.
Operating profit before special charges for the quarter ended June 30, 1998
increased 23% to $31.1 million from $25.3 million for the quarter ended June 30,
1997. The increase is due to the 1997 acquisition of the assets of Auto-Shade,
L.L.C. and Auto-Shade (Overseas) L.L.C. ("Axius") and Rain-X Corporation
("Rain-X") and improved margins in the lubricants business.

The special charges of $9.2 million (after-tax) in the second quarter of 1998
are comprised of $4 million (after-tax) of systems integration costs, $4.9
million (after-tax) of Pennzoil merger costs and $300,000 (after-tax) of
restructuring costs, which primarily relate to consulting fees.


                                       8
<PAGE>   9

Management's Discussion and Analysis of Results of Operations and Financial
Condition, continued

Sales and operating revenues were $312.9 million for the quarter ended June 30,
1998 and $319.3 million for the quarter ended June 30, 1997. The decrease in
sales can be attributed to the elimination of sales from the Company's West
Virginia refinery, which was sold in July 1997. This decrease has been partially
offset by the inclusion of Axius and Rain-X and the increase in car counts and
average ticket prices at the Company's Q Lube operations.

Lubricants and Lubricant Services operating profit before special charges was
$16.1 million for the quarter ended June 30, 1998, compared to $12.6 million for
the quarter ended June 30, 1997. This increase is primarily due to improved
margins as a result of product cost savings and a 6% increase in branded motor
oil volume. Sales and operating revenues for the quarter ended June 30, 1998
were $220 million, down 10% from $244.7 million for the quarter ended June 30,
1997. This decline reflects the elimination of $19.6 million of sales from the
Company's West Virginia refinery and an 11% decrease in private label and
controlled brand motor oil volume. A 7% and 4% increase in car counts and
average ticket prices at the Company's Q Lube operations replaced a portion of
these sales. The increased car counts are directly related to an increase in the
number of Q Lube stores operating in 1998.

Special charges in the second quarter of 1998 relating to Lubricants and
Lubricant Services were $3.6 million. The charges are comprised of $3.3 million
of systems integration costs and $262,000 of restructuring costs.

Consumer Products operating profit before special charges was $14.9 million for
the quarter ended June 30, 1998, compared to $12.7 million for the quarter ended
June 30, 1997. The increase is due to the inclusion of Axius and Rain-X
partially offset by softer additive volume. Sales and operating revenues for the
quarter ended June 30, 1998 were up 23% to $95.4 million, compared to $77.8
million for the quarter ended June 30, 1997. This increase is due to the
inclusion of $24.1 million of sales from Axius and Rain-X in 1998, offset by
lower additive volume.

Special charges in the second quarter of 1998 relating to the Consumer Products
segment were $3.6 million. The charges are comprised of $3.3 million of systems
integration costs and $262,000 of restructuring costs.

Interest expense increased $818,000 for the quarter ended June 30, 1998 as a
result of working capital needs and utilizing debt in the Company's 1997
acquisitions. Corporate expense was down to $5 million for the quarter ended
June 30, 1998 from $5.9 million for the quarter ended June 30, 1997. Special
charges in the first quarter of 1998 relating to corporate expense were $8.1
million, all of which are related to the Pennzoil merger.

The effective tax rate for the quarter ended June 30, 1998 of 47% for continuing
operations is higher than the 35% federal rate due to the impact of state and
foreign taxes and nondeductible amortization.

The Company reported net income of $3.4 million or $.09 per share for the six
months ended June 30, 1998, compared to net income of $15.7 million or $.45 per
share for the six months ended June 30, 1997. Net income includes charges of
$13.1 million (after-tax) relating to systems integration, merger and
restructuring. Net income for 1997 includes $2.4 million of income from the
Company's discontinued Truck-Lite operations. Operating profit before special
charges for the six months ended June 30, 1998 increased 13% to $52.2 million
from $46.2 million for the six months ended June 30, 1997. The increase is due
to the inclusion of Axius and Rain-X in 1998 and improved margins in the
lubricants business.


                                       9
<PAGE>   10

Management's Discussion and Analysis of Results of Operations and Financial
Condition, continued

The special charges of $13.1 million (after-tax) for the six months ended June
30, 1998 are comprised of $7.1 million (after-tax) of systems integration costs,
$5.3 million (after-tax) of Pennzoil merger costs and $716,000 (after-tax) of
restructuring costs, which primarily relate to consulting fees.

Sales and operating revenues were $611.4 million for the six months ended June
30, 1998 and $613.6 million for the six months ended June 30, 1997. The decrease
in sales can be attributed to the elimination of sales from the Company's West
Virginia refinery, which was sold in July 1997. This decrease has been partially
offset by the inclusion of Axius and Rain-X sales in 1998 and increases in car
counts and average ticket prices at the Company's Q Lube operations.

Lubricants and lubricant services operating profit before special charges was
$25.9 million for the six months ended June 30, 1998, compared to $21.3 million
for the six months ended June 30, 1997. This increase is primarily due to
improved margins as a result of product cost savings and an 8% increase in
branded motor oil volume. Sales and operating revenues for the six months ended
June 30, 1998 were $433.7 million, down 8% from $469.3 million for the six
months ended June 30, 1997. This decline reflects the elimination of $38.8
million of sales from the Company's West Virginia refinery and a 12% decrease in
private label and controlled brand motor oil volume. The increase in branded
motor oil and a 7% and 5% increase in car counts and average ticket prices at Q
Lube have partially offset the decrease in revenues. The increased car counts
are directly related to an increase in the number of Q Lube stores operating in
1998.

Special charges relating to Lubricants and Lubricant Services for the six months
ended June 30, 1998, were $6.4 million. The special charges are comprised of
$5.8 million of systems integration charges and $590,000 of restructuring
charges.

Consumer products operating profit before special charges was $26.3 million for
the six months ended June 30, 1998, compared to $24.9 million for the six months
ended June 30, 1997. The increase is due to the inclusion of Axius and Rain-X
partially offset by softer additive volume. The softer additive volumes can be
partially attributed to strong volumes in the fourth quarter of 1997. Sales and
operating revenues for the six months ended June 30, 1998 were $182.3 million,
compared to $149.3 million for the six months ended June 30, 1997. This increase
is primarily due to the inclusion of $41.2 million of sales from Axius and
Rain-X in 1998 offset by softer additive volumes.

Special charges in the first six months of 1998 relating to the Consumer
Products segment were $6.4 million. The charges are comprised of $5.8 million of
systems integration costs and $590,000 of restructuring costs.

For the six months ended June 30, 1998, corporate income was $264,000 compared
to $381,000 for the six months ended June 30, 1997. Interest expense increased
$1.5 million for the six months ended June 30, 1998 as a result of working
capital needs and utilizing debt in recent acquisitions. Corporate expenses
decreased to $10.1 million from $10.9 million for the six months ended June 30,
1997. Special charges in the first six months of 1998 relating to corporate
expense were $8.8 million, all of which relate to the Pennzoil merger.

The effective tax rate for the six months ended June 30, 1998 of 45.2% for
continuing operations is higher than the 35% federal rate due to the added
impact of state and foreign taxes and nondeductible amortization.


                                       10
<PAGE>   11

Management's Discussion and Analysis of Results of Operations and Financial
Condition, continued

On April 14, 1998, the Company, Pennzoil Company ("Pennzoil") and certain 
Pennzoil subsidiaries entered into an Agreement and Plan of Merger (the "Merger
Agreement"). The Merger Agreement and related agreements provide for the
separation of Pennzoil's motor oil, refined products and franchise operations
from its exploration and production operations and for the combination of the
motor oil, refined products and franchise operations with the Company. Closing
under the Merger Agreement is conditioned on, among other things, approval by
the Company's stockholders, expiration or termination of waiting periods under
the Hart-Scott-Rodino Antitrust Improvements Act of 1976 ("HSR Act"), and
receipt of a favorable tax ruling from the Internal Revenue Service. The waiting
period under the HSR Act expired on May 27, 1998.

The Merger Agreement, if consummated, would result in a Change of Control (as
defined in the Company's $400 million Credit Agreement). Under the terms of the
Credit Agreement, the Company would be required to notify each Bank (as defined
in the Credit Agreement) that a Change of Control has occurred within ten days
of such occurrence, and each Bank may terminate its Commitment (as defined in
the Credit Agreement) and declare the Note (as defined in the Company's Credit
Agreement) immediately due and payable with three Domestic Business Days (as
defined in the Credit Agreement) notice given not later than sixty days after
such Change of Control.

Cash and cash equivalents decreased by $6.7 million from December 31, 1997. The
decrease was comprised of $23.3 million of net cash used in operations, $30.2
million of net cash used in investing activities and $46.8 million of net cash
provided by financing activities. Cash used in operations was impacted by
additional working capital requirements, specifically an increase in accounts
receivable and a decrease in accrued liabilities of $34.6 million and $7.5
million and the payment of $5 million in Pennzoil merger costs.

Cash used in investing activities of $30.2 million was primarily due to $26.9
million in capital expenditures and acquisitions and the payment of taxes of
$12.3 million in connection with the Company's 1997 disposition of Truck-Lite.
Cash provided by financing activities of $46.8 million was impacted by a net
increase in debt of $52.4 million offset by payment of dividends of $7.3
million. The increase in debt was primarily due to working capital needs.

On July 29, 1998, the Board of Directors of the Company authorized a quarterly
dividend of $.10 per share, payable to shareholders of record as of August 15,
1998.

In June 1998, the Financial Accounting Standards Board issued Standard No. 133
"Accounting for Derivative Instruments and Hedging Activities." The Standard
establishes accounting and reporting standards for derivative instruments,
including certain derivative instruments embedded in other contracts,
(collectively referred to as derivatives) and for hedging activities. The new
Standard is effective for all fiscal quarters of all fiscal years beginning
after June 15, 1999. The Company does not expect the adoption of the new
Standard to have a material impact on its financial position or results of
operations.


PART II. OTHER INFORMATION
Item 1.  Legal Proceedings

Petrochem/Ekotek Superfund Site. As discussed in the Company's Annual Report on
Form 10-K for the year ended December 31, 1997, during December 1997, the United
States Environmental Protection Agency and the PRP group reached an agreement in
principle to perform remedial design/remedial action work. On April 27, 1998, a
consent decree was entered and the agreement became effective.


                                       11
<PAGE>   12

Legal Proceedings, continued

Slick 50. As discussed in the Company's Annual Report on Form 10-K for the year
ended December 31, 1997, the Company's subsidiary, Quaker State-Slick 50, Inc.
("Slick 50") and several Slick 50 subsidiaries and the Company in some instances
were named as defendants in a series of lawsuits filed on behalf of purported
classes of purchasers of Slick 50 engine treatment alleging that false,
misleading, deceptive and/or unsubstantiated advertising claims were made for
Slick 50 engine treatment.

The Company reached a settlement with counsel in all of the actions except one,
under which the Company will make available to class members $20 million in cash
rebates usable against future purchases of a variety of the products or services
of the Company and its subsidiaries and to pay attorneys' fees to counsel for
the class of $3.25 million. The Company will also pay all costs of notice and
settlement administration. The District Court for Dallas County, Texas, entered
an order approving the settlement on July 14, 1998.

Blue Coral. As discussed in the Company's Annual Report on Form 10-K for the
year ended December 31, 1997, John A. Garner and Steven G. Grant filed on their
own behalf and on behalf of a class of persons who purchased wax, polish or
protectant products sold by a number of defendants an action against a number of
car wax manufacturers including the Company's Blue Coral subsidiary, and certain
of its present and former officers. The complaint alleges that the defendants
falsely advertised and marketed such products and seeks treble damages,
attorneys' fees and costs for the class for alleged violations of the federal
Racketeer Influenced and Corrupt Organizations Act and compensatory damages for
alleged violations of the Ohio Consumer Sales Practices Act as well as for
breach of express warranty. The Company's motion to dismiss this action was
denied by the US District Court for the Northern District of Illinois on June
15, 1998 and an answer to the complaint was filed by the Company on July 21,
1998. The Company intends to vigorously contest this action; however, there can
be no assurance that the plaintiffs will not be awarded damages, some or all of
which may be payable by the Company.

Oil Changer. On July 28, 1998, Oil Changer, Inc. ("Oil Changer") and several
corporations affiliated with Oil Changer filed a suit in the Superior Court of
the State of California, Alameda County, against the Company, Herbert M. Baum,
John D. Barr, Conrad A. Conrad, Charles F. Bechtel and two other individuals.
The complaint alleges that the Company and Oil Changer were "strategic
partners" in an alleged partnership to develop quick lubrication centers in
Northern California. Oil Changer alleges that the Company breached the alleged
agreement by developing quick lubrication centers with another entity. The
complaint asserts claims for fraud, breach of fiduciary duty and usurpation of
partnership opportunity, partnership accounting, breach of contract, conspiracy 
and violation of Section 17200 of the California Business Professions Code.
Plaintiffs seek compensatory damages of $50 million, punitive damages,
restitution, attorneys' fees and costs as well as injunctive relief. The Company
intends to contest the action vigorously. There can be no assurance, however,
that the plaintiffs will not be awarded injunctive relief and/or damages, some
or all of which may be payable by the Company.

On July 28, 1998, Oil Changer and several corporations affiliated with Oil
Changer also filed a complaint in the United States District Court for the
Northern District of California against the Company and Pennzoil Company
(Pennzoil). The complaint asserts claims under Sections 1 and 2 of the Sherman
Act, Section 7 of the Clayton Act and Sections 16720 and 17200 of the California
Business Professions Code, alleging that the proposed merger of, the Company and
Pennzoil's downstream business will substantially lessen competition in, or
result in monopolization of, the markets for motor oil and quick lubrication
services in certain areas of California. Plaintiffs seek compensatory and treble
damages, restitution, attorneys' fees and costs as well as injunctive relief
enjoining the proposed merger. The Company intends to contest the action
vigorously. There can be no assurance, however, that the plaintiffs will not be
awarded injunctive relief and/or damages, some or all of which may be payable by
the Company.


                                       12
<PAGE>   13

Item 4. Submission of Matters to a Vote of Security Holders

On May 15, 1998, Quaker State held its Annual Meeting of Stockholders, at which
four items were submitted to a vote of security holders. The first item voted
upon was the election of directors, and the following individuals were elected
as directors, with the following votes for or withheld from each:

<TABLE>
<CAPTION>
      NAME                              VOTES FOR              VOTES WITHHELD
      ----                              ----------             --------------
<S>                                     <C>                       <C>    
John D. Barr                            32,877,942                552,994
Herbert M. Baum                         32,815,414                615,522
Leonard M. Carroll                      32,890,394                540,542
Conrad A. Conrad                        32,874,270                556,666
J. Taylor Crandall                      32,887,921                543,015
Laurel Cutler                           32,823,287                607,649
C. Frederick Fetterolf                  32,835,614                595,322
F. William Grube                        32,870,440                560,496
Forrest R. Haselton                     32,883,776                547,160
Kenneth Lee                             32,886,198                544,738
L. David Myatt                          32,869,860                561,076
Raymond A. Ross, Jr.                    32,863,089                567,847
Lorne R. Waxlax                         32,885,559                545,377
</TABLE>

The second matter submitted to a vote of security holders was a proposed award
of restricted stock to certain non-employee directors in lieu of retirement
benefits previously provided. On this matter, 24,774,275 shares were voted for
the proposition, 1,978,885 shares were voted against, and 316,498 shares
abstained.

The third matter submitted to a vote of security holders was the adoption of an
amendment to the Corporation's 1994 Stock Incentive Plan ("Plan") to authorize
the issuance under the Plan of 2,500,000 additional shares of the Corporation's
Capital Stock, $1.00 par value. On this third matter, 17,273,909 shares were
voted for the proposition, 9,497,142 shares were voted against, and 275,206
shares abstained.

The fourth matter submitted to a vote of security holders was the ratification
of the appointment of PricewaterhouseCoopers LLP as the Corporation's
independent auditors for 1998. On this fourth matter, 33,062,107 shares were
voted for the proposition, 159,015 shares were voted against, and 209,814 shares
abstained.


Item 6.  Exhibits and Reports on Form 8-K

(a) Exhibits

<TABLE>
<CAPTION>
EXHIBIT
  NO                                        DOCUMENT
-------                                     --------
<S>               <C>
11                Statement re Computation of Per Share Earnings (filed herewith).

12                Statement re Computation of Ratios (filed herewith).

27                Financial Data Schedule (filed herewith).
</TABLE>

----------
*      Management contract or compensatory plan, contract or arrangement
       required to be filed by Item 601 (b)(10)(iii) of Regulation S-K


                                       13
<PAGE>   14

Exhibits and Reports on Form 8-K, continued

(b) Reports on Form 8-K

The Company filed a current report on Form 8-K/A-2 on April 3, 1998, related to
its 1996 acquisition of Blue Coral, Inc. This report on Form 8-K/A-2 included
Pro Forma Consolidated Statement of Operations of the Company for the year ended
December 31, 1996.

The Company also filed a current report on Form 8-K on April 21, 1998, reporting
the proposed merger of the Company with a wholly owned subsidiary of Pennzoil
Company. No financial statements were included in this report on Form 8-K.


                                       14
<PAGE>   15

                    QUAKER STATE CORPORATION AND SUBSIDIARIES


                                   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.


                                         QUAKER STATE CORPORATION
                                               (Registrant)


Date        8/7/98                       By  /s/ Herbert M. Baum
            ---------------                  ----------------------------------
                                             Herbert M. Baum
                                             Chairman of the Board and
                                             Chief Executive Officer



Date        8/7/98                       By  /s/ Conrad A. Conrad
            ---------------                  ----------------------------------
                                             Conrad A. Conrad
                                             Vice Chairman and
                                             Chief Financial Officer


                                       15

<PAGE>   16
                            QUAKER STATE CORPORATION

                                  EXHIBIT LIST

        The following Exhibits are required to be filed with this quarterly
report on Form 10-Q.

<TABLE>
<CAPTION>
Exhibit No. and Document
------------------------
<S>             <C>
11              Statement re Computation of Per Share Earnings (filed herewith).

12              Statement re Computation of Ratios (filed herewith).

27              Financial Data Schedule (filed herewith).
</TABLE>

----------


                                       16