<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 September 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)
<TABLE>

<S>                                                                 <C>    
                      Delaware                                                 25-0742820
(State or other jurisdiction of incorporation of organization)      (IRS Employer Identification No.)
</TABLE>


                         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 October 31, 1998, 36,452,387 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                    Nine Months Ended
(in thousands except per share data, unaudited)            9/30/98          9/30/97           9/30/98          9/30/97
                                                       ---------------  ---------------   ---------------  ---------------
<S>                                                    <C>              <C>              <C>              <C>            
REVENUES
Sales and operating revenues                           $       296,509  $       303,356   $       907,917  $       916,983
Other, net                                                       3,531            1,132             6,111            4,551
                                                       ---------------  ---------------   ---------------  ---------------
                                                               300,040          304,488           914,028          921,534
                                                       ---------------  ---------------   ---------------  ---------------
COSTS AND EXPENSES
Cost of sales and operating costs                              183,340          194,710           551,836          590,311
Selling, general and administrative                             83,038           80,566           263,369          246,408
Depreciation and amortization                                   12,612           10,350            35,392           30,303
Interest                                                         7,385            7,189            21,899           20,251
Systems integration, merger,
    restructuring and other special charges                     10,929            5,291            32,603            5,291
                                                       ---------------  ---------------   ---------------  ---------------
                                                               297,304          298,106           905,099          892,564
                                                       ---------------  ---------------   ---------------  ---------------
Income from continuing operations before            
    income taxes                                                 2,736            6,382             8,929           28,970
Provision for income taxes                                       1,750            2,550             4,550           11,800
                                                       ---------------  ---------------   ---------------  ---------------
Income from continuing operations                                  986            3,832             4,379           17,170
Income from discontinued operations                                 --            1,477                --            3,848
                                                       ---------------  ---------------   ---------------  ---------------
NET INCOME                                             $           986  $         5,309   $         4,379  $        21,018
                                                       ===============  ===============   ===============  ===============

PER SHARE (BASIC AND DILUTED)
Income from continuing operations                      $           .03  $           .11   $           .12  $           .49
Income from discontinued operations                                 --              .04                --              .11
                                                       ---------------  ---------------   ---------------  ---------------
NET INCOME                                             $           .03  $           .15   $           .12  $           .60
                                                       ===============  ===============   ===============  ===============

Weighted average shares outstanding - Basic                     36,430           35,140            36,384           35,042
Weighted average shares outstanding - Diluted                   36,675           35,453            36,829           35,256
                                                       ===============  ===============   ===============  ===============

Dividends paid per share                               $           .10  $           .10   $           .30  $           .30
                                                       ===============  ===============   ===============  ===============

COMPREHENSIVE INCOME
Net income                                             $           986  $         5,309   $         4,379  $        21,018
Foreign currency translation adjustment,        
  net of tax                                                        56              188              (287)             271
                                                       ---------------  ---------------   ---------------  ---------------
Comprehensive income                                   $         1,042  $         5,497   $         4,092  $        21,289
                                                       ===============  ===============   ===============  ===============
</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>

NINE MONTHS ENDED SEPTEMBER 30
(in thousands, unaudited)                                                            1998                1997
                                                                              ---------------     ---------------
<S>                                                                           <C>                 <C>     
NET CASH PROVIDED BY OPERATING ACTIVITIES                                     $         6,498     $        22,609
                                                                              ---------------     ---------------
CASH FLOW FROM INVESTING ACTIVITIES
Capital expenditures                                                                  (28,494)            (45,087)
Proceeds from disposal of property and equipment and refinery                           6,132              36,764
Acquisition of businesses, net of cash acquired                                        (9,395)            (71,561)
Taxes paid on sale of discontinued operations                                         (12,250)                 --
Other, net                                                                              1,300              (3,343)
                                                                              ---------------     ---------------
     Net cash used in investing activities                                            (42,707)            (83,227)
                                                                              ---------------     ---------------
CASH FLOW FROM FINANCING ACTIVITIES
Dividends paid                                                                        (10,914)            (10,492)
Proceeds from debt                                                                     49,745             228,057
Payments on debt                                                                       (7,239)           (171,465)
Other, net                                                                              1,717                  --
                                                                              ---------------     ---------------
     Net cash provided by financing activities                                         33,309              46,100
                                                                              ---------------     ---------------
Net decrease in cash and cash equivalents                                              (2,900)            (14,518)
Total cash and cash equivalents at beginning of period                                 20,205              31,224
                                                                              ---------------     ---------------
TOTAL CASH AND CASH EQUIVALENTS AT END OF PERIOD                              $        17,305     $        16,706
                                                                              ===============     ===============
</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>

                                                                                September 30,      December 31, 
(in thousands, except share data)                                                   1998               1997
                                                                              ---------------     ---------------    
                                                                                 (unaudited)
<S>                                                                           <C>                 <C>            
ASSETS
Current assets:
Cash and cash equivalents                                                     $        17,305     $        20,205
Accounts and notes receivable, less allowance of $4,947 and
     $4,696 in 1998 and 1997                                                          197,636             186,654
Inventories                                                                            98,012              90,821
Other current assets                                                                   21,722              20,068
                                                                              ---------------     ---------------    
   Total current assets                                                               334,675             317,748
                                                                              ---------------     ---------------    
Property, plant and equipment, at cost                                                258,279             247,073
Goodwill, brands and other assets                                                     598,906             604,894
                                                                              ---------------     ---------------    
     TOTAL ASSETS                                                             $     1,191,860     $     1,169,715
                                                                              ===============     ===============    

LIABILITIES
Current liabilities:
Accounts payable                                                              $        69,095     $        70,805
Accrued liabilities                                                                   121,675             130,088
Debt payable within one year                                                            4,350              11,477
                                                                              ---------------     ---------------    
   Total current liabilities                                                          195,120             212,370
                                                                              ---------------     ---------------    
Long-term debt                                                                        478,528             429,198
Other long-term liabilities                                                           189,541             196,246
                                                                              ---------------     ---------------    
   Total liabilities                                                                  863,189             837,814
                                                                              ---------------     ---------------    
Commitments and contingencies

STOCKHOLDERS' EQUITY
Capital stock $1.00 par value; authorized shares, 250,000,000;
   issued shares, 38,224,651 and 37,977,144 in 1998 and 1997                           38,225              37,977
Additional capital                                                                    214,332             210,734
Retained earnings                                                                     105,916             112,451
Cumulative foreign currency translation adjustment                                       (154)                133
Treasury stock, at cost, 1,772,264 and 1,699,593 in 1998 and 1997                     (28,152)            (26,924)
Unearned compensation                                                                  (1,496)             (2,470)
                                                                              ---------------     ---------------    
   Total stockholders' equity                                                         328,671             331,901
                                                                              ---------------     ---------------    
     TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                               $     1,191,860     $     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                    Nine Months Ended
(in thousands, unaudited)                                  9/30/98          9/30/97           9/30/98          9/30/97
                                                       ---------------  ---------------   ---------------  ---------------  
<S>                                                    <C>              <C>               <C>              <C>            
REVENUES
Lubricants and lubricant services                      $       228,192  $       237,540   $       661,867  $       706,823
Consumer products                                               70,415           68,405           252,762          217,675
Intersegment sales                                              (2,098)          (2,589)           (6,712)          (7,515)
                                                       ---------------  ---------------   ---------------  ---------------  
Total operating revenues                               $       296,509  $       303,356   $       907,917  $       916,983
                                                       ===============  ===============   ===============  ===============  
OPERATING PROFITS
Lubricants and lubricant services                      $        18,529  $        11,292   $        44,417  $        32,563
Systems integration, merger,
    restructuring and other special charges                     (3,321)          (4,930)           (9,761)          (4,930)
                                                       ---------------  ---------------   ---------------  ---------------  
Total lubricants and lubricant services                         15,208            6,362            34,656           27,633
                                                       ---------------  ---------------   ---------------  ---------------  
Consumer products                                                5,701           11,036            32,043           35,921
Systems integration, merger,
    restructuring and other special charges                     (1,397)            (147)           (7,837)            (147)
                                                       ---------------  ---------------   ---------------  ---------------  
Total consumer products                                          4,304           10,889            24,206           35,774
                                                       ---------------  ---------------   ---------------  ---------------  
Total operating profits                                         19,512           17,251            58,862           63,407
Interest expense                                                (7,385)          (7,189)          (21,899)         (20,251)
Corporate other income                                             142              235               406              616
Corporate expense                                               (3,322)          (3,701)          (13,435)         (14,588)
Systems integration, merger,
    restructuring and other special charges                     (6,211)            (214)          (15,005)            (214)
                                                       ---------------  ---------------   ---------------  ---------------  
Total corporate expenses                                        (9,533)          (3,915)          (28,440)         (14,802)
                                                       ---------------  ---------------   ---------------  ---------------  
Income from continuing operations before
    income taxes                                       $         2,736  $         6,382   $         8,929  $        28,970
                                                       ===============  ===============   ===============  ===============
</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 $32.6 million for the nine months ended September 30,
     1998 are comprised of $14.5 million of systems integration costs, $15
     million of merger costs (see Note 8) and $3.1 million of restructuring and
     other special charges.

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 nine months ended September 30, 1998
     and 1997 is due to dilutive stock options of 245,000 and 313,000, and
     445,000 and 214,000, respectively.

5.   The following schedule is prepared on a pro forma basis as though Rain-X
     Corporation ("Rain-X") and the assets of Auto-Shade, L.L.C. and Auto-Shade
     (Overseas) L.L.C. ("Axius") 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 nine months ended September 30, 1997 (in thousands except per share data)
       ---------------------------------------------------------------------------------
       <S>                                                                                        <C>           
       Revenues                                                                                   $      964,364
       Income from continuing operations                                                                  19,024
       Income per share from continuing operations                                                           .53
                                                                                                  --------------
</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 $3.6 million
     at September 30, 1998 and $7.5 million at December 31, 1997. Inventories
     consist of:

<TABLE>
<CAPTION>

                                                                              September 30,       December 31, 
       (in thousands)                                                            1998                 1997
       --------------------------------                                      ---------------     --------------
<S>                                                                          <C>                 <C>           
       Lubricants and related materials                                      $        59,985     $       59,242
       Consumer products                                                              38,027             31,579
                                                                             ---------------     --------------
       Total                                                                 $        98,012     $       90,821
                                                                             ===============     ==============
</TABLE>

     Certain inventory quantities were reduced resulting in liquidation of LIFO
     inventory which increased net income by $1.6 million or $.04 per share for
     the nine months ended September 30, 1998.


                                       6


<PAGE>   7



NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS, CONTINUED

7.   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. The Company has filed an answer denying liability and a
     cross-complaint alleging breach by Oil Changer of a loan agreement with the
     Company and seeking damages and judicial foreclosure of the collateral held
     by the Company.

     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 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. On September 4, 1998, the Company filed a motion to
     dismiss this complaint, which was granted in part resulting in a dismissal
     of the claims under the California Business Professions Code and certain
     Sherman Act and Clayton Act claims. On October 8, 1998, Plaintiffs filed a
     notice of motion for a preliminary injunction to enjoin the proposed
     merger, to which the Company and Pennzoil filed a joint opposition.

     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.

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 Company's
     stockholders approved the merger at the Special Meeting of Stockholders
     held on September 18, 1998.


                                       7

<PAGE>   8



NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS, CONTINUED

     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 Credit Agreement) immediately due and payable with three
     Domestic Business Days (as defined in the Credit Agreement) notice given
     not later than ninety days after such Change of Control.


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 $986,000 or $.03 per share for the quarter
ended September 30, 1998, compared to net income of $5.3 million or $.15 per
share for the quarter ended September 30, 1997. The third quarter 1998 net
income includes charges of $6.6 million (after-tax) relating to systems
integration, merger, restructuring and other special charges. The third quarter
1997 net income includes special charges of $3.2 million (after-tax) and $1.5
million of income from the Company's discontinued Truck-Lite operations.
Operating profit before special charges for the quarter ended September 30, 1998
increased 9% to $24.2 million from $22.3 million for the quarter ended September
30, 1997. The increase is due to the 1997 acquisition of Rain-X Corporation
("Rain-X") and the assets of Auto-Shade, L.L.C. and Auto-Shade (Overseas) L.L.C.
("Axius") and improved margins in the lubricants business partially offset by
reduced Blue Coral/Slick 50 operating profits.

The special charges of $6.6 million (after-tax) in the third quarter of 1998 are
comprised of $1.7 million (after-tax) of systems integration costs, $3.8 million
(after-tax) of merger costs and $1.1 million (after-tax) of restructuring costs
and other special charges.

Sales and operating revenues were $296.5 million for the quarter ended September
30, 1998 and $303.4 million for the quarter ended September 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 and lower Slick 50
sales volume. This decrease has been partially offset by the inclusion of Axius
and Rain-X and increased sales at the Company's fast lube operations.

Lubricants and Lubricant Services operating profit before special charges was
$18.5 million for the quarter ended September 30, 1998, compared to $11.3
million for the quarter ended September 30, 1997. This increase is primarily due
to improved margins as a result of product cost savings and increased LIFO
profits of $1.4 million. Sales and operating revenues for the quarter ended
September 30, 1998 were $228.2 million, down 4% from $237.5 million for the
quarter ended September 30, 1997. This decline reflects the elimination of $7
million of sales from the Company's West Virginia refinery and an overall
decrease in motor oil volume of 6%. A 2% and 5% 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 third quarter of 1998 relating to Lubricants and
Lubricant Services were $3.3 million. The charges are comprised of $1.4 million
of systems integration costs and $1.9 million of other special charges.


                                       8


<PAGE>   9



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

Consumer Products operating profit before special charges was $5.7 million for
the quarter ended September 30, 1998, compared to $11 million for the quarter
ended September 30, 1997. The decrease is primarily due to the weak performance
of the Slick 50 business which resulted from competitive pressures that
intensified as Slick 50 complied with advertising restrictions agreed to with
the Federal Trade Commission. Sales and operating revenues for the quarter ended
September 30, 1998 were up 3% to $70.4 million, compared to $68.4 million for
the quarter ended September 30, 1997. This increase is due to the inclusion of
$18 million of sales from Axius and Rain-X in 1998, offset by lower Slick 50
sales volume.

Special charges in the third quarter of 1998 relating to the Consumer Products
segment were $1.4 million of systems integration costs.

Interest expense increased $196,000 for the quarter ended September 30, 1998 as
a result of working capital needs and utilizing debt in the Company's 1997
acquisitions. Corporate expense was down to $3.3 million for the quarter ended
September 30, 1998 from $3.7 million for the quarter ended September 30, 1997.
Special charges in the third quarter of 1998 relating to corporate expense were
$6.2 million of merger costs.

The effective tax rate for the quarter ended September 30, 1998 of 64% 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 $4.4 million or $.12 per share for the nine
months ended September 30, 1998, compared to net income of $21 million or $.60
per share for the nine months ended September 30, 1997. Net income includes
charges of $19.8 million (after-tax) relating to systems integration, merger,
restructuring and other special charges. Net income for 1997 includes special
charges of $3.2 million (after-tax) and $3.8 million of income from the
Company's discontinued Truck-Lite operations. Operating profit before special
charges for the nine months ended September 30, 1998 increased 12% to $76.5
million from $68.5 million for the nine months ended September 30, 1997. The
increase is due to the inclusion of Axius and Rain-X in 1998 and improved
margins in the lubricants business partially offset by reduced Blue Coral/Slick
50 operating profit.

The special charges of $19.8 million (after-tax) for the nine months ended
September 30, 1998 are comprised of $8.8 million (after-tax) of systems
integration costs, $9.2 million (after-tax) of merger costs and $1.8 million
(after-tax) of restructuring and other special charges.

Sales and operating revenues were $907.9 million for the nine months ended
September 30, 1998 and $917 million for the nine months ended September 30,
1997. The decrease in sales can be attributed to the elimination of $45.7
million 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 fast lube operations.

Lubricants and lubricant services operating profit before special charges was
$44.4 million for the nine months ended September 30, 1998, compared to $32.6
million for the nine months ended September 30, 1997. This increase is primarily
due to improved margins as a result of product cost savings, increased LIFO
profits of $2.7 million and a 3% increase in branded motor oil volume. Sales and
operating revenues for the nine months ended September 30, 1998 were $661.9
million, down 6% from $706.8 million for the nine months ended September 30,
1997. This decline reflects the elimination of sales from the Company's West
Virginia refinery and a 10% decrease in private label and controlled brand motor
oil volume. The increase in branded motor oil volume and a 5% increase in both
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.


                                       9


<PAGE>   10



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

Special charges relating to Lubricants and Lubricant Services for the nine
months ended September 30, 1998, were $9.8 million. The special charges are
comprised of $7.3 million of systems integration charges and $2.5 million of
restructuring and other special charges.

Consumer products operating profit before special charges was $32 million for
the nine months ended September 30, 1998, compared to $35.9 million for the nine
months ended September 30, 1997. The decrease is due to lower Slick 50 volume
partially offset by the inclusion of Axius and Rain-X. The lower Slick 50
volumes can be attributed to competitive pressures that intensified as Slick 50
complied with the advertising restrictions agreed to with the Federal Trade
Commission. Sales and operating revenues for the nine months ended September 30,
1998 were $252.8 million, compared to $217.7 million for the nine months ended
September 30, 1997. This increase is primarily due to the inclusion of $59.2
million of sales from Axius and Rain-X in 1998 offset by the lower Slick 50
volumes.

Special charges in the first nine months of 1998 relating to the Consumer
Products segment were $7.8 million. The charges are comprised of $7.2 million of
systems integration costs and $590,000 of restructuring costs.

Interest expense increased $1.6 million for the nine months ended September 30,
1998 as a result of working capital needs and utilizing debt in recent
acquisitions. Corporate expenses decreased to $13.4 million from $14.6 million
for the nine months ended September 30, 1997. Special charges in the first nine
months of 1998 relating to corporate expense were $15 million of merger costs.

The effective tax rate for the nine months ended September 30, 1998 of 51% for
continuing operations is higher than the 35% federal rate due to the added
impact of state and foreign taxes and nondeductible amortization.

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 Company's stockholders
approved the merger at the Special Meeting of Stockholders held on September 18,
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 ninety days after
such Change of Control.

Cash and cash equivalents decreased by $2.9 million from December 31, 1997. The
decrease was comprised of $6.5 million of net cash provided by operations, $42.7
million of net cash used in investing activities and $33.3 million of net cash
provided by financing activities. Cash provided by operations was impacted by
additional working capital requirements, specifically an increase in accounts
receivable and inventory of $16.7 million and $6.8 million, a net use of cash in
other assets and liabilities of $10.8 million and the payment of $7.2 million in
merger costs.



                                       10

<PAGE>   11



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

Cash used in investing activities of $42.7 million was primarily due to $37.9
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 $33.3 million was impacted by a net
increase in debt of $42.5 million offset by payment of dividends of $10.9
million. The increase in debt was primarily due to working capital needs.

On November 3, 1998, the Board of Directors of the Company authorized a
quarterly dividend of $.10 per share, payable December 15, 1998, to shareholders
of record as of November 15, 1998.

The Company continues to make progress in addressing the issue of computer
systems and embedded computer chips that are unable to accommodate the year 2000
and beyond.

The Company has completed reviews of computer systems and embedded technologies
at all its locations except its blending and packaging facilities. It is
expected that the assessment at these facilities will be completed by the end of
1998. In 1997, the Company initiated an SAP/R3 ("SAP") information systems
implementation project. The SAP information systems will enable the Company to
integrate the critical operational, administrative and customer service
functions of its lubricants and consumer products businesses. The SAP
information systems, which will be year 2000 compliant, are on schedule and are
expected to be fully operational by 1999 for the lubricants business.
Implementation of the SAP information systems at the Company's consumer products
businesses will be addressed subsequent to the merger. At this time, the Company
currently plans to have its critical systems compliant by the end of the second
quarter of 1999. Equipment utilizing embedded technology that is not year 2000
compliant will be replaced or renovated.

The Company has identified its critical customers, vendors and service providers
and is working with these third parties to mitigate any year 2000 issues. In
addition, the Company has contacted in writing its critical customers, vendors
and other service providers to ensure their systems are compliant. This
communication requested a written response from the customer, vendor or service
provider regarding their compliance with year 2000 issues. The Company is
currently reviewing the responses it has received. Appropriate follow-up will be
made if the response from a customer, vendor or service provider indicates a
problem with year 2000 compliance. Follow-up with critical customers, vendors
and other service providers who have not responded is also being done. 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 effect on the Company.

Contingency and test plans to mitigate the possible disruption in operations
from year 2000 issues are being developed and finalized. The Company currently
expects to complete the plans by the second quarter of 1999. The contingency
plans may include increasing inventory levels, obtaining alternate suppliers and
other appropriate measures.

As part of the Company's year 2000 program, a third-party consultant was hired
to review and assess the Company's year 2000 program once the program was
approximately 75% complete. The consultants have identified areas for
improvement in the Company's year 2000 program. These improvements are being
incorporated into the Company's year 2000 program. In addition, the consultants
continue to provide input regarding ongoing evaluations and development of
contingency plans.

The cost of year 2000 compliance including consulting fees, is not expected to
have a material effect on the Company's financial position. The Company
currently estimates the cost of year 2000 compliance including consulting fees
to be $1.5 million. Approximately $200,000 of the total expenditures will be of
a capital nature. The total cost expended for year 2000 compliance through
September 30, 1998, was $300,000. The remaining $1.2 million is expected to
primarily be incurred in the fourth quarter of 1998



                                       11

<PAGE>   12



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

and first quarter of 1999. These estimates do not include the cost of the SAP
project and the total cost associated with bringing the Company's blending and
packing facilities into compliance. The costs associated with the Company's
blending and packaging facilities will be finalized once the facilities have
completed their year 2000 review in the fourth quarter of 1998. Funds for the
year 2000 expenditures are expected to come from continuing operations or
borrowings under the Company's revolving credit agreement. Actual expenditures
may differ materially from the above estimates. Some factors that could cause
actual results to differ materially from estimates are: the availability of
resources, the Company's ability to identify and correct year 2000 issues and
the ability of customers, vendors and service providers to bring their systems
into year 2000 compliance.

The failure to correct a material year 2000 issue could result in an
interruption in, or a failure of, certain normal operations. Such failures could
materially affect the Company's results of operations, liquidity and financial
position. Due to the uncertainty inherent in the year 2000 problem, primarily
from the uncertainty of the year 2000 readiness of customers, vendors and other
service providers, the Company is unable to determine at this time whether the
consequences of year 2000 failures will have a material impact on the Company's
results of operations, liquidity or financial position. The Company's year 2000
program is expected to significantly mitigate the Company's level of uncertainty
about year 2000 issues. The Company believes that, with the implementation of
new computer systems and completion of the year 2000 program as scheduled, the
possibility of significant interruptions of normal operations should be reduced.

Certain aspects of the Company's year 2000 program included not upgrading or
replacing certain systems as they will be redundant if and when the merger with
Pennzoil is closed. Decisions regarding upgrade or replacement of certain
potentially redundant noncompliant systems have been delayed until after the
merger with Pennzoil closes. As with other noncompliant computer systems or
embedded technology, the Company will either convert or upgrade noncompliant
software or equipment, or discontinue the use of the noncompliant software or
equipment. If the announced merger with Pennzoil is not closed, these aspects
will be slightly behind the schedule established for the rest of the program.
The Company's readiness in these areas could be impacted if the merger is not
consummated or is not consummated timely.

The Company cautions investors that any forward-looking statements made by the
Company in the year 2000 update are not guarantees of future performance and
that actual results may differ materially from those in the forward-looking
statements.


PART II. OTHER INFORMATION
Item 1.  Legal Proceedings

Blue Coral. As reported 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 May 14,
1997 in the U.S. District Court for the Northern District of Illinois a
purported class action against a number of car wax manufacturers including the
Company's Blue Coral, Inc. subsidiary, and certain of its present and former
officers. The complaint alleges that the defendants falsely advertised and
marketed certain car wax and protectant products and seeks treble damages,
attorneys' fees and costs 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 Plaintiffs filed a motion for class certification on
August 20, 1998, which the defendants will oppose. 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.


                                       12


<PAGE>   13



Legal Proceedings, continued

Oil Changer. As reported in the Company's report on Form 10-Q for the quarter
ended June 30, 1998, 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. The Company has filed an answer denying liability and a
cross-complaint alleging breach by Oil Changer of a loan agreement with the
Company and seeking damages and judicial foreclosure of the collateral held by
the Company. 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.

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 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. On September 4, 1998, the Company filed a motion
to dismiss this complaint, which was granted in part resulting in a dismissal of
the claims under the California Business Professions Code and certain Sherman
Act and Clayton Act claims. On October 8, 1998, Plaintiffs filed a notice of
motion for a preliminary injunction to enjoin the proposed merger, to which the
Company and Pennzoil filed a joint opposition. 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.

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

On September 18, 1998, Quaker State held a Special Meeting of Stockholders, at
which the adoption of the Agreement and Plan of Merger, dated April 14, 1998, as
amended, among Pennzoil Company, Pennzoil Products Company, Downstream Merger
Company and Quaker State was submitted to a vote of security holders. A total of
26,508,555 shares were voted for the proposition, 1,099,776 shares were voted
against, and 175,024 shares abstained from voting.


                                       13


<PAGE>   14



Item 6.  Exhibits and Reports on Form 8-K

(a) Exhibits

<TABLE>
<CAPTION>
EXHIBIT
  NO.                                   DOCUMENT
-------                                 --------
<S>       <C>
10        Amendment to the Quaker State Corporation Severance Plan, adopted and
          effective as of September 30, 1998 (filed herewith).*

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

(b) Reports on Form 8-K

No Current Reports on Form 8-K were filed by Quaker State during the quarter
ended September 30, 1998.



                                       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     11/12/98                         By      /s/ Herbert M. Baum
      --------------                             ------------------------------
                                                  Herbert M. Baum
                                                  Chairman of the Board and
                                                  Chief Executive Officer



Date     11/12/98                         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>                                                    
10          Amendment to the Quaker State Corporation Severance Plan, adopted 
            and effective as of September 30, 1998 (filed herewith).

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