QUARTERLY REPORT UNDER SECTION 13 OR 15(d)
                      OF THE SECURITIES EXCHANGE ACT OF 1934


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


                                    FORM 10-Q
                         ----------------------------------


             [X] Quarterly Report Pursuant to Section 13 or 15(d) of
                       the Securities Exchange Act of 1934
                    For the period ended September 30, 1998
                    
                                       or

            [ ] Transition Report Pursuant to Section 13 or 15(d) of
                       the Securities Exchange Act of 1934
                          For the transition period from
                                       to
                            ----------    ---------

                        -------------------------------

                           Commission file number 0-7903


                 I.R.S. Employer Identification Number 36-2675371

                              QUIXOTE CORPORATION

                            (a Delaware Corporation)
                              One East Wacker Drive
                            Chicago, Illinois  60601
                           Telephone:  (312) 467-6755


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    XX        NO          
                                                     -------       -------

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date:  7,938,109 shares of the
Company's Common Stock ($.01-2/3 par value) were outstanding as of September
30, 1998.

                                    PART I
                            FINANCIAL INFORMATION

                    QUIXOTE CORPORATION AND SUBSIDIARIES
               Consolidated Condensed Statements of Operations
                                 (Unaudited)
<TABLE>
<CAPTION>
                                       Three Months Ended September 30,
                                       --------------------------------
                                           1998              1997
                                           ----              ----
<S>                                   <C>               <C>
Net sales.............................$ 16,063,000      $ 12,334,000
Cost of sales.........................   8,827,000         6,538,000
                                       -----------       -----------
Gross profit..........................   7,236,000         5,796,000

Operating expenses:
  Selling & administrative............   4,288,000         3,419,000
  Research & development..............     293,000           343,000
                                       -----------       -----------
                                         4,581,000         3,762,000

Operating profit......................   2,655,000         2,034,000
                                      
Other income (expense):
  Interest income.....................      39,000           235,000
  Interest expense....................    (168,000)           (1,000)
  Other...............................                         1,000
                                       -----------       -----------
                                          (129,000)          235,000
                                       -----------       -----------
Earnings before income taxes..........   2,526,000         2,269,000
Provisions for income taxes...........     884,000           681,000
                                       -----------       -----------
Net earnings..........................  $1,642,000        $1,588,000
                                       ===========       ===========

Basic earnings per share:
  Net earnings........................ $       .21       $       .20
                                       ===========       ===========
  Weighted average common shares 
    outstanding.......................   7,920,690         7,996,241
                                       ===========       ===========

Diluted earnings per share:
  Net earnings........................ $       .20       $       .20
                                       ===========       ===========
  Weighted average common shares 
    outstanding.......................   8,217,267         8,051,993
                                       ===========       ===========
<FN>
See Notes to Consolidated Condensed Financial Statements.
</TABLE>

                     QUIXOTE CORPORATION AND SUBSIDIARIES
                    Consolidated Condensed Balance Sheets

<TABLE>
<CAPTION>
                                                September 30,      June 30,
                                          ----------------------------------
ASSETS                                            1998               1998
----------------------------------------------------------------------------
                                               (Unaudited)
<S>                                           <C>              <C>
Current assets:
  Cash and cash equivalents...................$  1,555,000     $  3,927,000
  Accounts receivable, net of allowances
   for doubtful accounts of $568,000 at
   September 30 and $565,000 at June 30.......  11,652,000       13,976,000

  Refundable income taxes.....................                    1,132,000

  Inventories:
    Raw materials.............................   3,264,000        3,046,000
    Work in process...........................     776,000          696,000
    Finished goods............................   2,764,000        2,084,000
                                               -----------       -----------
                                                 6,804,000        5,826,000
                                               -----------       -----------

  Deferred income tax assets..................   1,642,000        1,642,000

  Other current assets........................     884,000          350,000
                                               -----------       -----------
Total current assets..........................  22,537,000       26,853,000
                                               -----------       -----------


Property, plant and equipment, at cost........  23,466,000       23,236,000
Less accumulated depreciation................. (10,193,000)      (9,754,000)
                                               -----------       -----------
                                                13,273,000       13,482,000
                                               -----------       -----------

Intangible assets.............................  12,334,000       12,553,000
Other assets..................................     893,000          987,000
Assets of discontinued operations.............   5,657,000        5,190,000
                                               -----------       -----------
                                              $ 54,694,000     $ 59,065,000
                                               ===========       ===========


<FN>
See Notes to Consolidated Condensed Financial Statements.
</TABLE>

                     QUIXOTE CORPORATION AND SUBSIDIARIES
                    Consolidated Condensed Balance Sheets
<TABLE>
<CAPTION>
                                               September 30,       June 30,
                                             -------------------------------
LIABILITIES AND SHAREHOLDERS' EQUITY             1998                1998
----------------------------------------------------------------------------
                                              (Unaudited)
<S>                                           <C>               <C> 
Current liabilities:
  Current portion of long-term debt.......... $   497,000       $    497,000
  Accounts payable...........................   1,459,000          1,681,000
  Dividends payable..........................                      1,021,000
  Accrued expenses...........................   3,119,000          3,894,000
  Income tax payable.........................     167,000
  Liabilities of discontinued operations.....                      4,614,000
                                               -----------       ----------- 
  
Total current liabilities....................   5,242,000         11,707,000
                                               -----------       -----------

Deferred income tax liabilities..............     795,000            795,000 
                                 

Long term debt, net of current portion.......   7,557,000          7,677,000

Shareholders' equity:
  Common stock...............................     150,000            148,000
  Capital in excess of par value of stock....  31,966,000         31,396,000
  Retained earnings..........................  16,966,000         15,324,000
  Treasury stock, at cost....................  (7,982,000)       (7,982,000)
                                              -----------        -----------
Total shareholders' equity...................  41,100,000         38,886,000
                                              -----------        -----------

                                             $ 54,694,000       $ 59,065,000
                                              ===========        ===========


<FN>
See Notes to Consolidated Condensed Financial Statements.
</TABLE>

                     QUIXOTE CORPORATION AND SUBSIDIARIES
               Consolidated Condensed Statements of Cash Flows
                                 (Unaudited)
<TABLE>
<CAPTION>
                                             Three Months Ended September 30
                                             -------------------------------
                                                       1998            1997
                                                       ----            ----
<S>                                                 <C>          <C>
Cash from operating activities:
Net earnings........................................$ 1,642,000  $ 1,588,000
Adjustments to reconcile net earnings to net cash
provided by operating activities:
  Depreciation......................................    439,000      407,000
  Amortization......................................    323,000      111,000
  Provisions for losses on accounts receivable......      3,000        3,000
  Changes in operating assets and liabilities:
    Accounts receivable.............................  2,321,000    (134,000)
    Refundable income taxes.........................  1,132,000    1,329,000 
 
    Inventories and other current assets............ (1,512,000)    (55,000)
    Accounts payable and accrued expenses...........   (997,000) (1,327,000)
    Income taxes payable............................    167,000       51,000
                                                     ----------  -----------
Net cash provided by operating activities of
  continuing operations.............................  3,518,000    1,973,000 

Net cash used in discontinued operations............ (4,727,000) (2,377,000)
                                                     ----------  ----------- 
Net cash used in operating activities............... (1,209,000)   (404,000)
                                                     ----------  -----------
Investing activities:
  Purchase of property, plant and equipment.........   (230,000)   (166,000)
  Other.............................................    (10,000)   (226,000)
                                                     ----------  ----------- 
Net cash used in investing activities...............   (240,000)    (392,000
                                                     ----------  -----------
Financing activities:
  Payments on notes payable.........................   (120,000)
  Payment of semi-annual cash dividend.............. (1,021,000) (1,039,000)
  Proceeds from exercise of stock options...........    218,000      68,000
  Repurchase of common stock for the treasury.......               (153,000) 
                                                      ---------- -----------
Net cash used in financing activities...............   (923,000) (1,124,000)
                                                      ---------- -----------
Decrease in cash and cash equivalents............... (2,372,000)  (1,920,000

Cash and cash equivalents at beginning of period....  3,927,000   18,463,000
                                                     ----------  -----------
Cash and cash equivalents at end of period..........$ 1,555,000  $16,543,000
                                                     ==========  ===========
<FN>
Note:  During the three months ended September 30, 1998, the Company had net
cash refunds of $415,000 for income taxes and paid $241,000 for interest. 
During the same period last year the Company had net cash refunds of
$700,000 for income taxes and paid $1,000 for interest.

See Notes to Consolidated Condensed Financial Statements.
</TABLE>


                      QUIXOTE CORPORATION AND SUBSIDIARIES
               Notes to Consolidated Condensed Financial Statements
                                   (Unaudited)

1.  The accompanying unaudited consolidated condensed financial statements
present information in accordance with generally accepted accounting
principles for interim financial information and applicable rules of
Regulation S-X.  Accordingly, they do not include all information or
footnotes required by generally accepted accounting principles for complete
financial statements.  Management believes the financial statements include
all normal recurring adjustments necessary for a fair presentation. 
Operating results for the three months ended September 30, 1998 do not
necessarily reflect the results that may be expected for the full year.  For
further information, refer to the consolidated financial statements and
notes thereto included in the Company=s Annual Report on Form 10-K for the
year ended June 30, 1998.

2.  During the second quarter of fiscal 1998, the Company adopted statement
of Financial Accounting Standards No. 128, Earnings Per Share.  SFAS No. 128
requires the presentation of basic earnings per share (EPS) and for
companies with potential dilutive securities, such as stock options and
warrants, diluted EPS.  SFAS No. 128 requires restatement of EPS for prior
periods.


The computation of basic and diluted earnings per share, as prescribed by
FASB 128, is as follows:
                                              Three Months Ended        
                                                 September 30,
<TABLE>
<CAPTION>
               
                                                1998         1997        
                                                ----         ----        
<S>                                            <C>          <C>
Net earnings per share of common stock:
    Basic ......................               $ .21        $  .20       
    Diluted ....................               $ .20        $  .20      

Numerator:
----------
Net earnings available to
  common shareholders-basic
  and diluted: .................         $ 1,642,000   $ 1,588,000 
                                          ==========    ==========   
Denominator:
------------
Weighted average shares
  outstanding-basic: ...........           7,920,690     7,996,241   

Effect of dilutive securities
  Options ......................             296,577        55,752      
                                          ----------    ----------      
Weighted average of shares
  outstanding-diluted ..........           8,217,267     8,051,993
                                          ==========    ========== 
</TABLE>
                   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                         CONDITION AND RESULTS OF OPERATIONS



CURRENT YEAR-TO-DATE VERSUS PRIOR YEAR-TO-DATE
----------------------------------------------

The Company's sales for the first quarter of fiscal 1999 increased 30% to
$16,063,000 from $12,334,000 in the first quarter last year due to both
internal sales growth as well as growth from two acquisitions the Company
completed during fiscal 1998.  Internal sales, without the effect from
acquisitions, increased 11% resulting from demand for Energy Absorption's
newer crash cushion products.  Energy Absorption=s permanent line of crash
cushion products increased due to strong unit sales of the newer QuadGuard
(Registered Trademark) family of crash cushions.  The QuadGuard family of 
products replaced the Company's GREAT(Registered Trademark) and GREAT 
CZ(Registered Trademark) crash cushion products.  Sales dollars of
the QuadGuard products increased at a lesser rate due to the lower selling
price of these products.  The Company also experienced sales increases in
its truck-mounted attenuator(TMA)product line, including the newer Alpha
100k TMA(Registered Trademark).  Sales of Safe-Hit's highway delineators 
and Spin-Cast's custom molded products also increased during the quarter.  
Roadway Safety Service, Inc. acquired in October 1997, contributed sales of 
$1,830,000 for the quarter.  Highway Information Systems, Inc. (HIS), 
acquired effective April 1, 1998, contributed sales of $596,000 for the 
current quarter.  Somewhat offsetting these sales increases, sales of the 
Energite(Registered Trademark) barrel product line and Triton 
Barrier(Registered Trademark) sales declined during the quarter. 

The gross profit margin in the first quarter of the current year decreased
to 45.0% from 47.0% in 1997.  This was due principally to a change in sales
mix from the GREAT crash cushion to the lower margin newer QuadGuard crash
cushion product line.  The QuadGuard family of products is priced lower than
the GREAT crash cushions.  Roadway Safety Service also contributed to the
decline in gross margin as its gross margin is lower than Energy
Absorption's historical gross margin. Offsetting this somewhat, HIS
contributed a higher gross margin than the Company=s average gross margin
but on much lower sales.

Selling and administrative expenses in the first quarter of the current year 
increased 25% to $4,288,000 from $3,419,000 in the first quarter last year. 
This was due principally to the fiscal 1998 acquisitions of Roadway Safety
Service and Highway Information Systems which added a combined $413,000 in
selling and administrative expenses.  Corporate level administrative
expenses increased $340,000 as a result of increased salaries and bonuses. 
Energy Absorption and its subsidiaries had a $115,000 increase in selling
and administrative expenses which was due to the increased level of its
sales. 

Research and development expenses in the current quarter of the current year
decreased 15% to $293,000 compared to $343,000 in the first quarter last
year.  This was due to an increased number of developmental projects
occurring in last year's first quarter.  During the current year, the
Company continued with its testing of a wider version of the Company's REACT
350 (Trademark) crash cushion as well as a snowplowable road marker and other
developmental products.

Interest income in the first quarter of the current year was $39,000
compared to $235,000 in the first quarter last year.  This interest income
declined as a result of a decline in the Company's invested cash from
$16,543,000 at September 30, 1997 to $1,555,000 at the end of the current
quarter.  Interest expense in the first quarter of the current year was
$168,000 compared to $1,000 in the first quarter last year.  Current period
interest expense relates both to seller financing in connection with the
acquisition of Roadway Safety Service as well as bank debt incurred in
connection with the acquisition of HIS. There was other expense of $1,000 in
the first quarter of last year.

The Company's effective income tax rate for the first quarter of the current
year was 35% compared to an effective income tax rate of 30% in the same
quarter last year due to last year's realization of certain tax benefits
along with the settlement of certain tax contingencies.  The Company
believes its effective income tax rate for the current year will be
approximately 35%. 


LIQUIDITY AND CAPITAL RESOURCES
-------------------------------

The Company had cash and cash equivalents of $1,555,000 and access to
additional funds of $36,500,000 under its bank arrangements as of September
30, 1998. Continuing operating activities were a source of cash for the
Company for the first quarter of fiscal 1999 providing $3,518,000. 
Discontinued operations however used cash of $4,727,000 primarily for a
legal settlement related to the Company's dispute with the Recording
Industry Association of America, and for other expenses including lease
commitments.  This resulted in a net cash use from operating activities of
$1,209,000.

Investing activities used cash of $240,000 during the current quarter
principally for the purchase of equipment for the Company's business.

Financing activities used cash of $923,000 during the current quarter.  The
payment of the Company's semi-annual cash dividend used cash of $1,021,000. 
The Company also used cash of $120,000 for payment of notes payable due in
connection with the acquisition of Roadway Safety Service.  Offsetting these
cash payments somewhat, the Company received cash of $218,000 for the
exercise of common stock options.

For fiscal 1999, the Company anticipates needing less than $2,500,000 in
cash for capital expenditures.  The Company may also need additional cash as
it considers acquiring businesses that complement its existing operations. 
Also, the Company will require additional investments in working capital to
maintain growth.  In addition, the Company may also need funds to repurchase
its own stock from time to time.  These expenditures will be financed either
through the Company's invested cash, cash generated from its operations, or
from borrowings available under the Company's revolving credit facility. 
The Company believes its existing cash, cash generated from operations and
funds available under its existing credit facility are sufficient for all
planned operating and capital requirements.

Year 2000 Issue
---------------------

During the current quarter, the Company continued in the process of making
an assessment of its Year 2000 (Y2K) issue relative to its own information
technology and non-information technology as well as assessing the state of
Y2K readiness of its vendors and customers.  The Company's Y2K task force,
consisting of senior management, continued to assess the Company's state of
readiness and to implement an action plan to correct Y2K deficiencies.  The
Company determined that its principal software programs for financial, order
entry and manufacturing planning is not Y2K compliant and began upgrading
these programs to more advanced versions that are Y2K compliant.  The
Company plans to complete implementation of this upgrade by December 1998.

In addition, the Company continued to evaluate the impact of the Y2K issue
on its non-information technology systems, such as manufacturing machinery,
equipment, computer-aided design and test equipment as well as products with
date sensitive software and embedded microprocessors.  The Company expects
to complete the assessment phase of its non-information technology systems
during its second fiscal quarter with remedial action planned for the
Company's third fiscal quarter.

The Company has plans to initiate communications with significant suppliers,
customers and other relevant third parties to identify and minimize
disruptions to the Company=s operations related to Y2K issues.  However,
there can be no certainty that the systems and products of other companies
on which the Company relies will not have a material adverse effect on the
Company's operations.  The Company expects to complete this assessment phase
during its third fiscal quarter.

The Company anticipates completing substantially all of its Y2K projects
during fiscal 1999.  In the event the Company falls short of these
milestones, additional internal resources will be focused on completing
these projects or developing contingency plans.  The estimated cost to
correct the Company's Y2K deficiencies is approximately $300,000.  This
estimate includes $200,000 in costs to upgrade its information technology
systems with the balance of the estimate for any changes or modifications
needed for non-information technology systems.  The Company estimates it has
spent approximately $75,000 to date.  While the Company believes that its
non-information technology and vendor and customer issues are of a lower
risk, until the Company's assessment of these risks is complete there can be
no assurance that these issues will not have a material effect on the
Company's operations.  All estimates of Year 2000 related costs are based on
numerous assumptions and there is no certainty that estimates will be
achieved and actual costs could be materially greater than anticipated.

In the event the Company is unable to take corrective measures related to
its Y2K issues, the Company's ultimate contingency plan is to outsource
critical computer applications where feasible and in addition create manual
systems until such corrective measurers are taken.  Please refer to the
Company's disclosure in its Form 10-K for the period ended June 30, 1998 for
additional information.


FORWARD LOOKING STATEMENTS
--------------------------

Various statements made within the Management's Discussion and Analysis of
Financial Condition and Results of Operations and elsewhere in this
Quarterly Report on Form 10-Q constitute "forward looking statements" for
purposes of the Securities and Exchange Commission's "safe harbor"
provisions under the Private Securities Litigation Reform Act of 1995 and
Rule 3b-6 under the Securities Exchange Act of 1934, as amended.  Investors
are cautioned that all forward looking statements involve risks and
uncertainties, including those detailed in the Company's filings with the
Securities and Exchange Commission.  There can be no assurance that actual
results will not differ from the Company's expectations.  Factors which
could cause materially different results include, among others,
uncertainties related to the introduction of the Company's products and
services; the successful completion and integration of acquisitions;  and
competitive and general economic conditions.



                                        II
                                OTHER INFORMATION


ITEM 1.  Legal Proceedings
--------------------------

Discovision Associates v. Disc Manufacturing, Inc., Case No. 95-21, U.S.
District Court for the District of Delaware.  On October 26, 1998, the Court
issued an Opinion and entered an Order finding that (1) five of the six
asserted patents were not infringed, (2) one patent was infringed and (3)
none of the patents were invalid.  DMI has requested clarification of the
order as it relates to DMI's equitable defenses and related antitrust case.

Feather v. Energy Absorption Systems, Inc., Case No. SCV-6077, Superior
Court of California.  After the jury verdict in favor of Energy Absorption
Systems, Inc. in August 1998, plaintiff agreed to waive all her appeal
rights in exchange for Energy Absorption's waiver of its right to seek
recovery of its costs and fees associated with its defense of this case.


ITEM 2. Changes in Securities
-----------------------------
None.

ITEM 3.  Default 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
-----------------------------------------
Reports on Form 8-K
None.


(b) Exhibits
None. 


                                SIGNATURE
                                ---------



Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this Quarterly Report on Form 10-Q for the
quarter ended September 30, 1998 to be signed on its behalf by the
undersigned thereunto duly authorized.


                                             QUIXOTE CORPORATION



DATE: November 12, 1998                     /S/ Daniel P. Gorey
      -----------------                     ------------------------------
                                             DANIEL P. GOREY
                                             Vice President, Chief Financial
                                             Officer and Treasurer
                                             (Chief Financial & Accounting 
                                             Officer)