UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                        WASHINGTON, D.C. 20549

                              FORM 10-Q



     Quarterly Report pursuant to Section 13 or 15(d) of the Securities
Exchange Act of 1934

[x]         FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1999

                                  OR


[ ]  Transition Report pursuant to Section 13 or 15(d) of the Securities
     Exchange Act of 1934

          For the transition period from . . . . to . . . .


                    Commission file number 1-7627



                       FRONTIER OIL CORPORATION
        (Exact name of registrant as specified in its charter)


         WYOMING                                      74-1895085
(State or other jurisdiction of                    (I.R.S. Employer
incorporation or organization)                     Identification No.)


 10000 MEMORIAL DRIVE, SUITE 600                       77024-3411
      HOUSTON, TEXAS                                   (Zip Code)
(Address of principal executive offices)


  Registrant's telephone number, including area code: (713) 688-9600


                                   
        ------------------------------------------------------
        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 (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.  Yes [x]  No . . .

Registrant's number of common shares outstanding as of April 23, 1999:
 27,281,124



                       FRONTIER OIL CORPORATION
                    QUARTERLY REPORT ON FORM 10-Q
                 FOR THE QUARTER ENDED MARCH 31, 1999


                                INDEX

                                                                 Page
                                                                 ----
Part I - Financial Information

   Item 1.  Financial Statements                                    1

   Item 2.  Management's Discussion and Analysis of Financial
            Condition and Results of Operations                     6

Part II - Other Information                                        10



FORWARD-LOOKING STATEMENTS

This Form 10-Q contains "forward-looking statements" within the meaning of
Section 27A of the Securities Act and Section 21E of the Securities Exchange Act
of 1934, as amended (the "Exchange Act"), including, without limitation,
statements that include the words "anticipates," "believes," "could,"
"estimates," "expects," "intends," "may," "plan," "predict," "project,"
"should," and similar expressions, and statements relating to the Company's
strategic plans, capital expenditures, industry trends and prospects and the
Company's financial position.  Such forward-looking statements involve known and
unknown risks, uncertainties and other factors that may cause actual results,
performance or achievements of the Company to differ materially from those
expressed or implied by such forward-looking statements.  Although the Company
believes that its plans, intentions and expectations reflected in such
forward-looking statements are reasonable, it can give no assurance that such
plans, intentions or expectations will be achieved. Important factors that could
cause actual results to differ materially from the Company's expectations
("Cautionary Statements") are set forth under the caption "Management's
Discussion and Analysis of Financial Condition and Results of Operations," and
elsewhere in this document.  All subsequent written and oral forward-looking
statements attributable to the Company or persons acting on its behalf are
expressly qualified in their entirety by the Cautionary Statements.




Definitions of Terms

bbl(s) = barrel(s)
bpd = barrel(s) per day



                    PART I - FINANCIAL INFORMATION

ITEM 1. FINANCIAL STATEMENTS

FRONTIER OIL CORPORATION AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF OPERATIONS 
(Unaudited, in thousands except per share amounts)



                                                                      
For the three months ended March 31,                             1999       1998
                                                              ---------  ---------
                                                                   

Revenues:
  Refined products                                            $  55,945  $  69,023
  Other                                                             272        668
                                                              ---------  ---------
                                                                 56,217     69,691
                                                              ---------  ---------

Costs and Expenses:
  Refining operating costs                                       54,441     64,190
  Selling and general expenses                                    2,077      1,994
  Depreciation                                                    2,841      2,376
                                                              ---------  ---------
                                                                 59,359     68,560
                                                              ---------  ---------

Operating Income (Loss)                                          (3,142)     1,131
Interest Expense, net                                             1,627      1,970
                                                              ---------  ---------

Income (Loss) Before Income Taxes                                (4,769)      (839)
Provision For Income Taxes                                           77          -
                                                              ---------  ---------

Income (Loss) Before Extraordinary Item                          (4,846)      (839)

Extraordinary Loss on Retirement of Debt, net of taxes                -      3,013
                                                              ---------  ---------

Net Income (Loss)                                             $  (4,846) $  (3,852)
                                                              =========  =========
Basic and Diluted Earnings (Loss) Per Share of Common Stock:
  Continuing Operations                                       $    (.18) $    (.03)
  Extraordinary Loss                                                  -       (.11)
                                                              ---------  ---------
  Net Income (Loss)                                           $    (.18) $    (.14)
                                                              =========  =========




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

                                    - 1 -



FRONTIER OIL CORPORATION AND SUBSIDIARIES
CONSOLIDATED BALANCE SHEETS
(Unaudited, in thousands except shares)



                                                                      
March 31, 1999 and December 31, 1998                            1999       1998
                                                             ---------  ---------
                                                                  

ASSETS
Current Assets:
  Cash, including cash equivalents of
   $21,593 in 1999 and $31,781 in 1998                       $  23,461  $  33,589
  Trade and other receivables, less allowance for
   doubtful accounts of $500 in 1999 and 1998                   16,231     11,021
  Inventory of crude oil, products and other                    26,447     20,269
  Other current assets                                             462        560
                                                             ---------  ---------
   Total current assets                                         66,601     65,439
                                                             ---------  ---------
Property, Plant and Equipment, at cost:
  Refinery and pipeline                                        166,557    164,664
  Furniture, fixtures and other equipment                        3,430      3,426
                                                             ---------  ---------
                                                               169,987    168,090
   Less - Accumulated depreciation                              59,055     56,217
                                                             ---------  ---------
                                                               110,932    111,873

Other Assets                                                     5,406      4,714
                                                             ---------  ---------

                                                             $ 182,939  $ 182,026
                                                             =========  =========

LIABILITIES AND SHAREHOLDERS' EQUITY
Current Liabilities:
  Accounts payable                                           $  27,012  $  23,492
  Revolving credit facility                                     11,200      3,800
  Accrued turnaround cost                                        1,658      1,339
  Accrued liabilities and other                                  2,405      4,280
  Accrued interest                                                 810      2,403
                                                             ---------  ---------
   Total current liabilities                                    43,085     35,314
                                                             ---------  ---------

Long-Term Debt, net of current maturities:
   9-1/8% Senior Notes                                          70,000     70,000

Deferred Credits and Other                                       5,882      5,238

Deferred Income Taxes                                            1,121      1,121

Commitments and Contingencies

Shareholders' Equity:
  Preferred stock, $100 par value, 500,000 shares
   authorized, no shares issued
  Common stock, no par, 50,000,000 shares authorized,
   28,487,024 and 28,385,584 shares issued in 1999 and 1998     57,289     57,278
  Paid-in capital                                               86,770     86,305
  Retained earnings (deficit)                                  (74,907)   (70,061)
  Treasury stock, 1,196,700 shares and 605,700 shares
   in 1999 and 1998                                             (6,301)    (3,169)
                                                             ---------  ---------
  Total Shareholders' Equity                                    62,851     70,353
                                                             ---------  ---------

                                                             $ 182,939  $ 182,026
                                                             =========  =========


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

                                    - 2 -


FRONTIER OIL CORPORATION AND SUBSIDIARIES
CONSOLIDATED STATEMENTS OF CASH FLOWS
(Unaudited, in thousands)



                                                                         
For the three months ended March 31,                          1999       1998
                                                           ---------  ---------
                                                                

OPERATING ACTIVITIES
Net income (loss)                                          $  (4,846) $  (3,852)
Depreciation                                                   2,841      2,376
Deferred credits and other                                       (62)       207
Extraordinary loss on retirement of debt                           -      3,013
Change in working capital from operations                    (10,574)    (7,706)
                                                           ---------  ---------
  Net cash used in operating activities                      (12,641)    (5,962)
                                                           ---------  ---------

INVESTING ACTIVITIES
Additions to property and equipment                           (1,914)    (3,097)
Other                                                           (250)         -
                                                           ---------  ---------
  Net cash used in investing activities                       (2,164)    (3,097)
                                                           ---------  ---------

FINANCING ACTIVITIES
Borrowings:
  Refining credit facility                                     7,400      5,700
  9-1/8% Senior Notes                                              -     70,000
Repayments of debt:                                     
  12% Senior Notes, including redemption premium                   -    (25,423)
  7-3/4% Convertible Subordinated Debentures, including
   redemption premium                                              -    (45,971)
Debt issuance costs                                                -     (2,700)
Issuance of common stock                                         476        195
Purchase of treasury stock                                    (3,143)      (284)
Other                                                            (56)       (61)
                                                           ---------  ---------
  Net cash provided by financing activities                    4,677      1,456
                                                           ---------  ---------

Increase (decrease) in cash and cash equivalents             (10,128)    (7,603)
Cash and cash equivalents, beginning of period                33,589     21,735
                                                           ---------  ---------
Cash and cash equivalents, end of period                   $  23,461  $  14,132
                                                           =========  =========
   

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

                                    - 3 -


FRONTIER OIL CORPORATION AND SUBSIDIARIES
NOTES TO INTERIM FINANCIAL STATEMENTS
March 31, 1999
(Unaudited)

1.  FINANCIAL STATEMENT PRESENTATION 

FINANCIAL STATEMENT PRESENTATION

    The condensed consolidated financial statements include the accounts of
Frontier Oil Corporation, a Wyoming Corporation, and its wholly owned
subsidiaries, including Frontier Holdings Inc. (the "Refinery"), collectively
referred to as Frontier or the Company.  These financial statements have been
prepared by the registrant without audit, pursuant to the rules and regulations
of the Securities and Exchange Commission (SEC) and include all adjustments
(comprised of only normal recurring adjustments) which are, in the opinion of
management, necessary for a fair presentation.  Certain information and footnote
disclosures normally included in financial statements prepared in accordance
with generally accepted accounting principles have been condensed or omitted
pursuant to such rules and regulations, although the Company believes that the
disclosures are adequate to make the information presented not misleading.  It
is suggested that the financial statements included herein be read in
conjunction with the financial statements and the notes thereto included in the
Company's annual report on Form 10-K for the year ended December 31, 1998.

    Frontier conducts its refining operations in the Rocky Mountain region of
the United States.  The Company's Cheyenne, Wyoming Refinery purchases the crude
oil to be refined and markets the refined petroleum products produced, including
various grades of gasoline, diesel fuel, asphalt and petroleum coke.

EARNINGS PER SHARE

        Basic and diluted earnings per share have been computed based on the
weighted average number of common shares outstanding and did not assume the
exercise of stock option shares for the diluted computation as a loss from
continuing operations was incurred.  The basic and diluted average shares
outstanding for the three months ended March 31, 1999 and 1998 were 27,589,539
and 28,104,335 respectively.

NEW ACCOUNTING STATEMENT

    In June 1998, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 133, "Accounting for Derivative Instruments
and Hedging Activities".  The Statement establishes accounting and reporting
standards requiring that every derivative instrument (including certain
derivative instruments embedded in other contracts) be recorded in the balance
sheet as either an asset or liability measured at its fair value.  The Statement
requires that changes in the derivative's fair value be recognized currently in
earnings unless specific hedge accounting criteria are met.  Special accounting
for qualifying hedges allows a derivative's gains and losses to offset related
results on the hedged item in the income statement, and requires that a company
must formally document, designate, and assess the effectiveness of transactions
that receive hedge accounting.

    Statement 133 is effective for fiscal years beginning after June 15, 1999. A
 company may also implement the Statement as of the beginning of any fiscal
 quarter after issuance (that is, fiscal quarters beginning June 16, 1998 and
 thereafter).  Statement 133 cannot be applied retroactively. Statement 133 must
 be applied to  (a) derivative instruments and (b) certain derivative
 instruments embedded in hybrid contracts that were issued, acquired, or
 substantively modified after December 31, 1997 (and, at the company's election,
 before January 1, 1998).

    The Company plans to adopt Statement 133 as of January 1, 2000 and presently
does not expect the impact of adopting Statement 133 to be material.

                                    - 4 -



2.  SCHEDULE OF MAJOR COMPONENTS OF INVENTORY



                                                 March 31,    December 31,
                                                   1999          1998
                                                ---------      ---------
                                                      (in thousands)
                                                         

Crude oil                                       $   4,821      $   1,407
Unfinished products                                 5,170          2,644
Finished products                                   8,887          8,602
Chemicals                                           1,457          1,333
Repairs and maintenance supplies and other          6,112          6,283
                                                ---------      ---------
                                                $  26,447      $  20,269
                                                =========      =========



                                    - 5 -




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

                          RESULTS OF OPERATIONS
 THREE MONTHS ENDED MARCH 31, 1999 COMPARED WITH THE SAME PERIOD IN 1998

   The Company had a loss for the three months ended March 31, 1999 of $4.8
million, or $.18 per share, compared to a loss of $3.9 million, or $.14 per
share, for the same period in 1998.  The 1998 results included a $3.0 million
extraordinary loss on early retirement of debt.
 
   Operating income decreased $4.3 million in 1999 versus 1998 due to a decrease
in the refined product spread (revenues less material costs) of $3.1 million, a
decrease in other income of $396,000, and increases in refining operating
expenses of $206,000, selling and general costs of $83,000 and depreciation of
$465,000.

   Refined product revenues and refining operating costs are impacted by changes
in the price of crude oil.  The average price of crude oil was lower in 1999
than in 1998.  The refined product spread was $4.05 per bbl compared to $4.74
per bbl in 1998.  The 1999 refined product spread decreased due to lower margins
and a  reduction in the light/heavy crude spread offset by inventory gains.
High nationwide levels of gasoline and diesel inventories in 1999 have kept
margins for gasoline and diesel low.  Frontier's market place was accordingly
impacted with decreases from the first quarter of 1998 in average gasoline and
diesel margins of 35% and 13%, respectively. Commencing in late March, product
margins began their seasonal improvement, but margins are  lagging expectations
due to high nationwide and local inventory levels.

   The price of crude oil reached its low point in December 1998 when crude
closed at below $10.75 per bbl on the New York Mercantile Exchange and stayed at
or below $13.00 per bbl during January and February 1999. Commencing in March,
with the announcement of OPEC production cuts, the price of crude oil increased
and ended March at $16.76 per bbl.  In 1999, the Company realized a benefit to
the refined product spread of approximately $2.8 million because of inventory
gains.  In 1998, the Company realized inventory losses of approximately $3.7
million because of declines in crude oil prices.  Inventories are recorded at
the lower of cost on a first in, first out (FIFO) basis or market.

   The light/heavy spread was $1.94 per bbl for the three months ended March 31,
1999, the lowest ever experienced by Frontier.  The tightening spread has been
caused by low crude oil prices and the resulting reduced supply of heavy crude
oil as certain heavy crude oil has been uneconomic to produce.  With the recent
increase in crude oil prices, more heavy crude oil has become available for
purchase, although the price remains high relative to lighter crude.  Because of
the higher cost of heavy crude oil, more lighter crude has been purchased and
fewer heavy bbls have been contracted for at a fixed price above postings than
in prior years and the length of the 1999 contracts shortened to mainly average
three to six months.  Consequently, any sustained improvement in crude oil
prices may enable the Company to purchase a higher percentage of heavy crude oil
and benefit from an improvement in the light/heavy spread.

   Refined product revenues decreased $13.1 million or 19%.  The decrease in
refined product revenues resulted from a $3.71 per bbl decrease in average
gasoline sales prices, a $3.79 per bbl decrease in average diesel sales prices
and a refined product sales volumes decrease of 4% in 1999 from 1998 levels.
Yields of gasoline decreased 11% while yields of diesel decreased 23% in 1999
compared to the same period in 1998.  The decline in yields and sales volumes
during 1999 were caused by the 14 day crude unit turnaround which commenced
March 14, 1999 and was completed March 27, 1999.

   Other income decreased $396,000 to $272,000 in 1999 versus 1998 due to sulfur
credit sales in 1998 of $360,000.

   Refining operating costs decreased $9.7 million or 15% from 1998 levels due
to a decrease in material costs offset by an increase in refining operating
expenses.  Material costs per bbl decreased 16% or $2.23 per bbl in 1999
primarily due to lower oil prices which more than offset an increases in
material costs from the use of a lower percentage of less expensive heavy crude
oil and a lower light/heavy spread. During 1999, the Refinery decreased its use
of heavy crude oil by 27% and the heavy crude oil utilization rate expressed as
a percentage of total crude oil decreased to 79% in 1999 from 93% in 1998.  The
light/heavy spread decreased 59% to average $1.94 per bbl in the three months of
1999.  Refining operating expense per bbl increased $.20 per bbl to $ 3.61 per
bbl in 1999 due to slightly higher expenses related to turnaround accruals and
fewer sales bbls.

   Selling and general expenses increased $83,000 or 4% for the three months
ended March 31, 1999.

   Depreciation increased $465,000 or 20% in the 1999 three-month period as
compared to the same period in 1998, attributable to increases in capital
investment.

                                    - 6 -



   The interest expense decrease of $343,000 or 17% in 1999 was attributable to
utilizing proceeds of the 9-1/8% Senior Notes to retire the remaining 12% Senior
Notes in March 1998.  Average debt for the three months decreased from $94
million in 1998 to $77 million in 1999.

   Income tax expense for 1999 is for state income taxes.

                     LIQUIDITY AND CAPITAL RESOURCES

   Net cash used in operating activities was $12.6 million and $6.0 million for
the three months ended March 31, 1999 and 1998, respectively.  Working capital
changes required $10.6 million and $7.7 million of cash flows for the first
three months of 1999 and 1998, respectively.  During 1999, increases in
receivables, inventory and payables occurred due to rising crude oil prices.
Consistent with the seasonality of its business, the Company invests in working
capital during the first half of the year and recovers working capital
investment in the second half of the year. In addition to normal seasonality,
working capital cash flows were used as inventory quantities of crude oil and
intermediate products increased because of the March turnaround.  During 1998,
working capital cash flows were used to increase gasoline and diesel inventories
in preparation for the April 1998 turnaround.

   At March 31, 1999, the Company had $23.5 million of cash and $7.9 million
available under the its line of credit.  The Company had working capital of
$23.5 million at March 31, 1999.

   Additions to property and equipment in the first three months of 1999 of $1.9
million decreased $1.2  million from the first three months in 1998. Capital
expenditures of approximately $9.0 million are planned in 1999.

   On September 1, 1998, the Company announced that the Board of Directors had
approved a stock repurchase program of up to three million shares of common
stock.  In 1998, 469,700 shares of common stock were purchased by the Company
for $2.3 million. Through March 1999, an additional 593,500 shares of common
stock have been purchased by the Company for $3.1 million.

                                YEAR 2000

   Many of the computer systems used by the Company today were designed and
developed using two digits, rather than four, to specify the year.  As a result,
such systems will recognize the year 2000 as "00".  This could cause many
computer applications to fail completely or to create erroneous results unless
corrective measures are taken.  The Company utilizes software and related
information technology ("IT") essential to its operations that may be affected
by the Year 2000 issue.  The company also relies on non-IT systems in its daily
operations, such as fax machines, radios, voice mail systems, alarms, monitors
and other miscellaneous systems.  Additionally the company is dependent upon
third party relationships with both suppliers and customers.

    The Company initiated a company wide task force to assess and resolve the
business risks associated with the Year 2000 issues.  The process implemented by
the task force included identification of possibly effected systems, assessment
of probability of and implications of noncompliance, alternative modifications
to or replacements of existing systems or technology and cost and timetables for
completion.  The analysis is being substantially completed by internal resources
with third party vendor verification when available.

   The Company has completed a preliminary review of its IT, accounting and
operational, systems for Year 2000 compliance.  The review of the Company's
primary financial computer systems, including its accounting system, indicated
only minor modifications will be required to make them Year 2000 compliant.  The
process control system has been documented as Year 2000 compliant by the vendor
literature but further testing is being pursued to verify this. The Company
believes it will be able to implement the necessary corrections to all of its
critical information technology and non-IT systems by mid 1999 with one
exception.  The weigh scale software will be upgraded in October 1999 to avoid
disrupting high volume seasonal operations.  Systems identified as non-critical
noncompliant will be addressed at later dates.

   The Company does significant business with and is dependent upon various
third party entities.  These relationships include customers, critical suppliers
of products and utilities, financial institutions, transportation companies and
others.  The Company is also reviewing the possible impact of Year 2000
noncompliance by its outside providers.  Communications with critical third
parties regarding their plans and progress addressing the Year 2000 has been
initiated and continues.  The Company is dependent upon the reliability and
completeness of the third parties representations in assessing their Year 2000
readiness.

   The estimated costs of the software and hardware modifications and
some consultant support identified to date will be between $65,000 to $150,000
to implement and will be financed from operating cash flows.

                                    - 7 -



Expenditures through March 31, 1999 totaled approximately $32,500.  The Company
does not separately track the internal costs for the Year 2000 project, and such
costs are principally the related payroll costs for its information systems
group.

   The Company's refinery operations are very dependent upon outside providers
and in certain areas an alternative to the Company is not available.  Failure to
correct a material year 2000 issue could result in an interruption in, or a
failure of, certain normal business activities or operations.  Although the
Company is taking steps to reduce the likelihood of interruption or failure of
normal operations, there can be no guarantee that other companies' systems, on
which our systems rely, will be timely Year 2000 compliant. To date, the Company
is not aware of any significant Year 2000 problems with these outside providers
that would have a material adverse effect on the Company's business or results
of operations, liquidity and financial operations.

   The Company is in the process of developing contingency plans to address
issues associated with the reasonably likely worst case scenarios.  The Company
expects to have such contingency plans formulated by the end of August 1999.

                                    - 8 -




REFINING OPERATING STATISTICAL INFORMATION



                                                             Three Months Ended
                                                                  March 31,
                                                            --------------------
                                                               1999       1998
                                                            ---------  ---------
                                                                 

Raw material input (bpd)
  Light crude                                                   6,400      2,293
  Heavy crude                                                  24,032     32,729
  Other feed and blend stocks                                   5,946      6,333
                                                            ---------  ---------
   Total                                                       36,378     41,355

Manufactured product yields (bpd)
  Gasoline                                                     15,366     17,268
  Diesel                                                       10,886     14,228
  Asphalt and other                                             8,652      9,047
                                                            ---------  ---------
   Total                                                       34,904     40,543

Total product sales (bpd)
  Gasoline                                                     21,390     21,176
  Diesel                                                       11,484     12,492
  Asphalt and other                                             5,691      6,625
                                                            ---------  ---------
   Total                                                       38,565     40,293

Operating margin information (per sales bbl)
  Average sales price                                       $   16.12  $   19.04
  Material costs (under FIFO inventory accounting)              12.07      14.30
                                                            ---------  ---------
   Product spread                                                4.05       4.74
  Operating expenses excluding depreciation                      3.61       3.41
  Depreciation                                                    .81        .65
                                                            ---------  ---------
   Operating margin (loss)                                  $    (.37) $     .68

Manufactured product margin before depreciation (per bbl)   $     .50  $    1.33

Purchased product margin (per purchased product bbl)        $    (.47) $    1.48

Light/heavy crude spread (per bbl)                          $    1.94  $    4.72

Average sales price (per sales bbl)
  Gasoline                                                  $   18.11  $   21.82
  Diesel                                                        16.99      20.78
  Asphalt and other                                              9.34       6.84



                                    - 9 -



                       PART II - OTHER INFORMATION

ITEM 1.   Legal Proceedings -

          None, which in the opinion of management would have a material
          impact on the registrant.

ITEM 2.   Changes in Securities -

          There have been no changes in the constituent instruments defining the
          rights of the holders of any class of registered securities during the
          current quarter.
             
ITEM 3.   Defaults Upon Senior Securities -

          None.

ITEM 4.   Submission of Matters to a Vote of Security Holders -

          None.

ITEM 5.   Other Information -

          None.

ITEM 6.   Exhibits and Reports on Form 8-K -

          (a) Exhibits

          10.01 - Executive Employment Agreement dated February 25, 1999 between
                  the Company and James R. Gibbs.

          10.02 - Executive Employment Agreement dated February 25, 1999 between
                  the Company and Julie H. Edwards.

          10.03 - Executive Employment Agreement dated February 25, 1999 between
                  the Company and S. Clark Johnson.

          10.04 - Executive Employment Agreement dated February 25, 1999 between
                  the Company and J. Currie Bechtol.

          10.05 - Executive Employment Agreement dated February 25, 1999 between
                  the Company and Gerald B. Faudel.

          10.06 - Executive Employment Agreement dated February 25, 1999 between
                  the Company and Jon D. Galvin.

          27    - Financial Data Schedule

          (b) Reports on Form 8-K

          None.
          
                                    - 10 -


                               SIGNATURES

   Pursuant to the requirements of Section 13 or 15(d) 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.


                            FRONTIER OIL CORPORATION




                            By: /s/Jon D. Galvin
                                ---------------------------
                                Jon D. Galvin
                                Vice President - Controller
                             





Date: April 28, 1999