<PAGE>   1
                       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 March 31, 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 April 30, 1998, 36,415,483 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>
THREE MONTHS ENDED MARCH 31
(in thousands except per share data, unaudited)                                     1998              1997
===========================================================================     ============      ============
<S>                                                                             <C>               <C>         
REVENUES
Sales and operating revenues                                                    $    298,529      $    294,353
Other, net                                                                             1,629             2,057
                                                                                ------------      ------------
                                                                                     300,158           296,410
                                                                                ------------      ------------
COSTS AND EXPENSES
Cost of sales and operating costs                                                    183,867           191,759
Selling, general and administrative                                                   88,711            78,838
Depreciation and amortization                                                         11,353             9,741
Interest                                                                               6,959             6,326
Restructuring, systems integration and other special charges                           6,425                --
                                                                                ------------      ------------
                                                                                     297,315           286,664
                                                                                ------------      ------------
Income from continuing operations before income taxes                                  2,843             9,746
Provision for income taxes                                                             1,225             3,975
                                                                                ------------      ------------
Income from continuing operations                                                      1,618             5,771
Income from discontinued operations                                                       --             1,094
                                                                                ------------      ------------
NET INCOME                                                                      $      1,618      $      6,865
                                                                                ============      ============

PER SHARE (BASIC AND DILUTED)
Income from continuing operations                                               $        .04      $        .17
Income from discontinued operations                                                       --               .03
                                                                                ------------      ------------
NET INCOME                                                                      $        .04      $        .20
                                                                                ============      ============

Weighted average shares outstanding - Basic                                           36,298            34,868
Weighted average shares outstanding - Diluted                                         36,574            34,970
                                                                                ============      ============

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

COMPREHENSIVE INCOME
Net income                                                                      $      1,618      $      6,865
Foreign currency translation adjustment, net of tax                                     (103)              (33)
                                                                                ------------      ------------
Comprehensive income                                                            $      1,515      $      6,832
                                                                                ============      ============
</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>
THREE MONTHS ENDED MARCH 31
(in thousands, unaudited)                                                           1998              1997
===========================================================================     ============      ============
<S>                                                                             <C>               <C>          
     Net cash used in operating activities                                      $    (25,536)     $     (7,657)
                                                                                ------------      ------------
CASH FLOW FROM INVESTING ACTIVITIES
Capital expenditures                                                                  (8,903)          (15,746)
Proceeds from disposal of property and equipment                                         420               295
Acquisition of businesses, net of cash acquired                                       (4,965)           (7,699)
Taxes paid on sale of discontinued operations                                        (12,250)               --
Other, net                                                                             3,809            (4,762)
                                                                                ------------      ------------
     Net cash used in investing activities                                           (21,889)          (27,912)
                                                                                ------------      ------------
CASH FLOW FROM FINANCING ACTIVITIES
Dividends paid                                                                        (3,628)           (3,466)
Proceeds from debt                                                                    49,915            24,717
Payments on debt                                                                      (6,599)             (668)
Other, net                                                                             1,157                --
                                                                                ------------      ------------
     Net cash provided by financing activities                                        40,845            20,583
                                                                                ------------      ------------
Net decrease in cash and cash equivalents                                             (6,580)          (14,986)
Total cash and cash equivalents at beginning of period                                20,205            29,397
                                                                                ------------      ------------
TOTAL CASH AND CASH EQUIVALENTS AT END OF PERIOD                                $     13,625      $     14,411
                                                                                ============      ============
</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>
                                                                                        March 31,        December 31,
(in thousands, except share data)                                                          1998               1997
==================================================================================     ============      ============
                                                                                        (unaudited)
<S>                                                                                    <C>               <C>         
ASSETS
Current assets:
Cash and cash equivalents                                                              $     13,625      $     20,205
Accounts and notes receivable, less allowance of $4,659 and
     $4,696 in 1998 and 1997                                                                205,312           186,654
Inventories                                                                                 100,445            90,821
Other current assets                                                                         19,750            20,068
                                                                                       ------------      ------------
   Total current assets                                                                     339,132           317,748
                                                                                       ------------      ------------
Property, plant and equipment, at cost                                                      251,710           247,073
Goodwill, brands and other assets                                                           606,895           604,894
                                                                                       ------------      ------------
     TOTAL ASSETS                                                                      $  1,197,737      $  1,169,715
                                                                                       ============      ============

LIABILITIES
Current liabilities:
Accounts payable                                                                       $     74,453      $     70,805
Accrued liabilities                                                                         111,295           130,088
Debt payable within one year                                                                  5,224            11,477
                                                                                       ------------      ------------
   Total current liabilities                                                                190,972           212,370
                                                                                       ------------      ------------
Long-term debt                                                                              478,767           429,198
Other long-term liabilities                                                                 196,650           196,246
                                                                                       ------------      ------------
   Total liabilities                                                                        866,389           837,814
                                                                                       ------------      ------------
Commitments and contingencies

STOCKHOLDERS' EQUITY
Capital stock $1.00 par value; authorized shares, 250,000,000;
   issued shares, 38,054,244 and 37,977,144 in 1998 and 1997                                 38,054            37,977
Additional capital                                                                          211,814           210,734
Retained earnings                                                                           110,441           112,451
Cumulative foreign currency translation adjustment                                               30               133
Treasury stock, at cost, 1,699,593 in 1998 and 1997                                         (26,924)          (26,924)
Unearned compensation                                                                        (2,067)           (2,470)
                                                                                       ------------      ------------
   Total stockholders' equity                                                               331,348           331,901
                                                                                       ------------      ------------
     TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                                        $  1,197,737      $  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>
THREE MONTHS ENDED MARCH 31
(in thousands, unaudited)                                                           1998              1997
===========================================================================     ============      ============
<S>                                                                             <C>               <C>         
REVENUES
Lubricants and lubricant services                                               $    213,671      $    224,538
Consumer products                                                                     86,968            71,475
Intersegment sales                                                                    (2,110)           (1,660)
                                                                                ------------      ------------
Total operating revenues                                                        $    298,529      $    294,353
                                                                                ============      ============
OPERATING PROFITS
Lubricants and lubricant services                                               $      9,758      $      8,668
     Restructuring, systems integration and other special charges                     (2,856)               --
                                                                                ------------      ------------
Total lubricants and lubricant services                                                6,902             8,668
                                                                                ------------      ------------
Consumer products                                                                     11,409            12,191
     Restructuring, systems integration and other special charges                     (2,856)               --
                                                                                ------------      ------------
Total consumer products                                                                8,553            12,191
                                                                                ------------      ------------
Total operating profits                                                               15,455            20,859
Interest expense                                                                      (6,959)           (6,326)
Corporate other income                                                                   141               190
Corporate expense                                                                     (5,081)           (4,977)
     Restructuring, systems integration and other special charges                       (713)               --
                                                                                ------------      ------------
Total corporate expenses                                                              (5,794)           (4,977)
                                                                                ------------      ------------
Income from continuing operations before income taxes                           $      2,843      $      9,746
                                                                                ============      ============
</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 $6.4 million in the first quarter of 1998 are comprised
     of $5 million of systems integration costs, $713,000 of merger costs (see
     Note 7) and $665,000 of restructuring costs.

3.   The effective tax rates of 43.1% and 40.8% for the three month periods
     ended March 31, 1998 and 1997 are higher than the 35% federal statutory
     rate due to the impact of state and foreign taxes and nondeductible
     amortization.

4.   The following schedule is prepared on a pro forma basis as though
     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 three months ended March 31, 1997 (in thousands except per share data)
--------------------------------------------------------------------------------------------
<S>                                                                             <C>         
Revenues                                                                        $    311,879
Income from continuing operations                                                      5,749
Income per share from continuing operations                                              .16
                                                                                ============
</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.

5.   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 $6.6 
     million at March 31, 1998 and $7.5 million at December 31, 1997. 
     Inventories consist of:

<TABLE>
<CAPTION>
                                                         March 31,      December 31,
(in thousands)                                             1998             1997
--------------------------------------------------     ------------     ------------
<S>                                                    <C>              <C>         
Lubricants and related materials                       $     61,769     $     59,242
Consumer products                                            38,676           31,579
                                                       ------------     ------------
Total                                                  $    100,445     $     90,821
                                                       ============     ============
</TABLE>



                                       6
<PAGE>   7

NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS, CONTINUED

6.   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. These actions seek damages on
     behalf of the purported classes. 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 has reached a tentative settlement with
     counsel in all of the class actions except one, under which the Company
     would 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 as approved by the court but not in any event to exceed $3.25
     million. The Company will also pay all costs of notice and settlement
     administration. The District Court for Dallas County, Texas, preliminarily
     approved the tentative settlement on March 16, 1998, with the final
     approval hearing set for July 13, 1998. The tentative settlement of the
     class action suits would fulfill the consumer redress requirements under
     the FTC consent decree.

     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.   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, and receipt of a favorable tax ruling from the
     Internal Revenue Service.

     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.




                                       7
<PAGE>   8




NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS, CONTINUED

8.   Effective January 1, 1998, the Company adopted Statement of Financial
     Accounting Standards No. 130 "Reporting Comprehensive Income" ("SFAS No.
     130"), which establishes new guidance for the reporting and display of
     comprehensive income and its components: the adoption had no impact on the
     Company's net income or stockholders' equity. SFAS No. 130 requires that
     the Company's foreign currency translation adjustment be included in other
     comprehensive income. The provisions of SFAS No. 130 have been applied to
     the prior period presentation.

     In March 1998, Statement of Position 98-1 "Accounting for the Costs of
     Computer Software Developed or Obtained for Internal Use" ("SOP 98-1") was
     issued. SOP 98-1 is effective for fiscal years beginning after December 15,
     1998, and should be applied to internal-use computer software costs
     incurred in those fiscal years for all projects, including those projects
     in progress upon initial application of SOP 98-1. This statement of
     position will require the Company to change its method of accounting for
     internal-use computer software costs. The Company currently expenses all
     costs in connection with the development and/or acquisition of internal-use
     computer software, except license fees. SOP 98-1 will require the Company
     to capitalize certain of these costs subsequent to adoption. The Company
     will adopt SOP 98-1 January 1, 1999.


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 $1.6 million or $.04 per share for the
quarter ended March 31, 1998, compared to net income of $6.9 million or $.20 per
share for the quarter ended March 31, 1997. The first quarter 1998 net income
includes $3.9 million (after-tax) of charges relating to restructuring, systems
integration and other special charges. The first quarter 1997 net income
includes $1.1 million of income from the Company's discontinued Truck-Lite
operations.

Special charges of $3.9 million (after-tax) in the first quarter of 1998 are
comprised of $3.1 million (after-tax) of systems integration costs, $434,000
(after-tax) of Pennzoil merger costs and $400,000 (after-tax) of restructuring
costs, which primarily relate to consulting fees.

Sales and operating revenues were $298.5 million for the quarter ended March 31,
1998 and $294.4 million for the quarter ended March 31, 1997. The increase in
sales can be attributed to the Company's 1997 acquisitions of Axius and Rain-X
and the increase in car counts and average ticket prices at the Company's Q Lube
operations. The increased car counts are directly related to an increase in the
number of Q Lube stores operating in 1998. The increases more than offset the
loss of sales from the Company's West Virginia refinery, which was sold in July
1997.

Operating profit before restructuring, systems integration and other special
charges for the quarter ended March 31, 1998 increased 1% to $21.2 million from
$20.9 million for the quarter ended March 31, 1997.




                                       8
<PAGE>   9

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

Lubricants and Lubricant Services operating profit before special charges was
$9.8 million for the quarter ended March 31, 1998, compared to $8.7 million for
the quarter ended March 31, 1997. This increase is primarily due to improved
margins as a result of product cost savings and improved branded motor oil
volume. Revenues for the quarter ended March 31, 1998 were $213.7 million, down
5% from $224.5 million for the quarter ended March 31, 1997. This decline
reflects the loss of $20 million of sales from the Company's West Virginia
refinery. A portion of these sales was replaced by a 10% increase in branded
motor oil volume, an 8% increase in Q Lube car counts and a 5% increase in Q
Lube average ticket prices.

Special charges in the first quarter of 1998 relating to Lubricants and
Lubricant Services were $2.9 million. The charges are comprised of $2.5 million
of systems integration costs and $332,000 of restructuring costs.

Consumer Products operating profit before special charges was $11.4 million for
the quarter ended March 31, 1998, compared to $12.2 million for the quarter
ended March 31, 1997. The decrease is due to a change in product mix, strong
automotive appearance product volume and softer additive volume, coupled with an
increase in advertising and marketing expenses. The softer additive volumes can
be attributed to strong volumes in the fourth quarter of 1997. Revenues for the
quarter ended March 31, 1998 were up 22% to $87 million, compared to $71.5
million for the quarter ended March 31, 1997. This increase is due to strong
automotive appearance product volume and the inclusion of $17 million of
revenues from Axius and Rain-X in 1998. These increases were partially offset by
lower additive volume.

Special charges in the first quarter of 1998 relating to the Consumer Products
segment were $2.9 million. The charges are comprised of $2.5 million of systems
integration costs and $332,000 of restructuring costs.

Interest expense increased for the quarter ended March 31, 1998 as a result of
utilizing debt in the Company's 1997 acquisitions. Corporate expense was up
slightly to $5.1 million for the quarter ended March 31, 1998 from $5 million
for the quarter ended March 31, 1997. Special charges in the first quarter of
1998 relating to corporate expense were $713,000. The charges are related to the
Pennzoil merger.

The effective tax rate of 43.1% for continuing operations is higher than the 35%
federal rate due to the 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, and receipt of a
favorable tax ruling from the Internal Revenue Service.

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
<PAGE>   10




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

Cash and cash equivalents decreased by $6.6 million from December 31, 1997. The
decrease was comprised of $25.5 million of net cash used in operations, $21.9
million of net cash used in investing activities and $40.8 million of net cash
provided by financing activities. Cash used in operations was impacted by
additional working capital requirements, specifically increases in accounts
receivable and inventory of $23 million and $9.6 million.

Cash used in investing activities of $21.9 million was primarily due to $13.9
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 $40.8 million was impacted by a net
increase in debt of $43.3 million offset by payment of dividends of $3.6
million. The increase in debt was due to working capital needs.

On March 26, 1998 the Board of Directors of the Company authorized a quarterly
dividend of $.10 per share, payable to shareholders of record as of May 15,
1998.

In March 1998, Statement of Position 98-1 "Accounting for the Costs of Computer
Software Developed or Obtained for Internal Use" ("SOP 98-1") was issued. SOP
98-1 is effective for fiscal years beginning after December 15, 1998, and should
be applied to internal-use computer software costs incurred in those fiscal
years for all projects, including those projects in progress upon initial
application of SOP 98-1. This statement of position will require the Company to
change its method of accounting for internal-use computer software costs. The
Company currently expenses all costs in connection with the development and/or
acquisition of internal-use computer software, except license fees. SOP 98-1
will require the Company to capitalize certain of these costs subsequent to
adoption. The Company will adopt SOP 98-1 January 1, 1999.

PART II. OTHER INFORMATION
Item 1.  Legal Proceedings

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 have
been 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 has reached a tentative settlement with counsel in all of the
actions except one, under which the Company would 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 as approved by the court but not in any
event to exceed $3.25 million. The Company will also pay all costs of notice and
settlement administration. The District Court for Dallas County, Texas,
preliminarily approved the tentative settlement on March 16, 1998, with the
final approval hearing set for July 13, 1998.




                                       10
<PAGE>   11




Item 6.  Exhibits and Reports on Form 8-K

(a) Exhibits

EXHIBIT
  NO                                                         DOCUMENT

        10(a)   Third Amendment to the Quaker State Corporation 1994 Stock
                Incentive Plan, dated April 14, 1998 (filed herewith).*

        10(b)   Amendment to the Quaker State Corporation Pension Plan, Salaried
                Employees Plan Document amending Article XI thereof effective
                April 14, 1998 (filed herewith). *

        10(c)   Amendment to the Quaker State Corporation Pension Plan,
                Hourly-Classified Employees Plan Document amending Article XI
                thereof effective April 14, 1998 (filed herewith). *

        10(d)   Fourth Amendment to Employment Agreement between Quaker State
                Corporation and Herbert M. Baum, dated April 14, 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).

--------
*       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

The Company filed a current report on Form 8-K/A-2 on April 4, 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.



                                       11
<PAGE>   12

                    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    5/12/98                            By  /s/ Herbert M. Baum
      --------------------                     -----------------------------
                                               Herbert M. Baum
                                               Chairman of the Board and
                                               Chief Executive Officer



Date    5/12/98                            By  /s/ Conrad A. Conrad
      --------------------                     -----------------------------
                                               Conrad A. Conrad
                                               Vice Chairman and
                                               Chief Financial Officer




                                       12

<PAGE>   13
                            QUAKER STATE CORPORATION

                                  EXHIBIT LIST

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

Exhibit No. and Document

10(a)   Third Amendment to the Quaker State Corporation 1994 Stock Incentive
        Plan, dated April 14, 1998 (filed herewith). *

10(b)   Amendment to the Quaker State Corporation Pension Plan, Salaried
        Employees Plan Document amending Article XI thereof effective April 14,
        1998 (filed herewith). *

10(c)   Amendment to the Quaker State Corporation Pension Plan,
        Hourly-Classified Employees Plan Document amending Article XI thereof
        effective April 14, 1998 (filed herewith). *

10(d)   Fourth Amendment to Employment Agreement between Quaker State
        Corporation and Herbert M. Baum, dated April 14, 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).


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



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