<PAGE>
 
================================================================================

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

                                   FORM 10-Q

  (Mark One)
    [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
                             EXCHANGE ACT OF 1934

                 For the quarterly period ended MARCH 31, 1998

                                      OR

    [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
                             EXCHANGE ACT OF 1934

                        Commission file number 1-12147

                           DELTIC TIMBER CORPORATION
            (Exact name of registrant as specified in its charter)

          Delaware                                      71-0795870
(State or other jurisdiction of          (I.R.S. Employer Identification Number)
incorporation or organization)


  210 East Elm Street, P. O. Box 7200,                  71731-7200
        El Dorado, Arkansas
(Address of principal executive offices)                (Zip Code)

      Registrant's telephone number, including area code:  (870) 881-9400

Securities registered pursuant to Section 12(b) of the Act:


       Title of each class             Name of each exchange on which registered

   Common Stock, $.01 Par Value               New York Stock Exchange, Inc.

 Series A Participating Cumulative            New York Stock Exchange, Inc.
 Preferred Stock Purchase Rights

     Securities registered pursuant to Section 12(g) of the Act:  None

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    .
                            ---      ---

Number of shares of Common Stock, $.01 Par Value, outstanding at April 30, 1998,
was 12,813,879.





================================================================================
<PAGE>
 
            TABLE OF CONTENTS - FIRST QUARTER 1998 FORM 10-Q REPORT


                                                                           Page
                                                                          Number
                                                                          ------

                        PART I -  FINANCIAL INFORMATION

Item 1.  Financial Statements                                                 3

Item 2.  Management's Discussion and Analysis of Financial
         Condition and Results of Operations                                 11
 
 
                          PART II - OTHER INFORMATION
 
Item 1.  Legal Proceedings                                                   13
Item 2.  Change in Securities                                                13
Item 3.  Defaults Upon Senior Securities                                     13
Item 4.  Submission of Matters to a Vote of Security Holders                 13
Item 5.  Other Information                                                   13
Item 6.  Exhibits and Reports on Form 8-K                                    13
Signatures                                                                   14
 

                                       2
<PAGE>
 
                        PART I - FINANCIAL INFORMATION

ITEM 1.   FINANCIAL STATEMENTS

                           DELTIC TIMBER CORPORATION
                               AND SUBSIDIARIES
                          Consolidated Balance Sheets
                        -------------------------------
                            (Thousands of dollars)

                                                            March 31,   Dec. 31,
                                                                1998       1997
                                                           ---------   --------
                                                          (unaudited)
Assets                                                   
 Current assets                                          
  Cash and cash equivalents                                 $ 23,460     31,045
  Trade accounts receivable - net                              5,054      3,772
  Other receivables                                            1,259        297
  Inventories                                                  6,936      8,595
  Prepaid expenses and other current assets                    2,525      2,060
                                                            --------    -------
   Total current assets                                       39,234     45,769
                                                         
 Investment in real estate held for development and sale      20,483     20,365
 Investment in and advances to Del-Tin Fiber, L.L.C.           6,911      7,383
 Timber and timberlands - net                                118,041    108,206
 Property, plant, and equipment - net                         40,741     39,646
 Deferred charges and other assets                             3,663      4,006
                                                            --------    -------
                                                         
   Total assets                                             $229,073    225,375
                                                            ========    =======
                                                         
Liabilities and Stockholders' Equity                     
 Current liabilities                                     
  Current maturities of long-term debt                      $    204      1,801
  Notes payable                                                  356        192
  Trade accounts payable                                       2,988      2,542
  Accrued taxes other than income taxes                        1,313        979
  Bank overdraft                                               1,631      1,479
  Other accrued liabilities                                      815        805
  Income taxes payable                                         1,626          -
                                                            --------    -------
   Total current liabilities                                   8,933      7,798
                                                         
 Long-term debt                                                  889      1,093
 Deferred credits and other noncurrent liabilities             6,750      6,488
 Redeemable preferred stock                                   30,000     30,000
 Stockholders' equity                                    
  Preferred stock                                                  -          -
  Common stock                                                   128        128
  Capital in excess of par value                              68,834     68,372
  Retained earnings                                          113,935    111,496
  Unamortized restricted stock awards                           (396)         -
                                                            --------    -------
   Total stockholders' equity                                182,501    179,996
                                                            --------    -------
                                                         
   Total liabilities and stockholders' equity               $229,073    225,375
                                                            ========    =======

See accompanying notes to consolidated financial statements.

                                       3
<PAGE>
 
                           DELTIC TIMBER CORPORATION
                               AND SUBSIDIARIES
                 Consolidated Statements of Income (Unaudited)
                         Three Months Ended March 31,
            -------------------------------------------------------
               (Thousands of dollars, except per share amounts)
 
 
                                                     1998      1997
                                                  -------   -------
 
Net sales                                         $27,008    24,364
                                                  -------   -------
                                                           
Costs and expenses                                         
 Cost of sales                                     17,138    13,655
 Depreciation, amortization, and                           
   cost of fee timber harvested                     1,729     1,260
 General and administrative expenses                1,752     1,634
                                                  -------   -------
                                                           
   Total costs and expenses                        20,619    16,549
                                                  -------   -------
                                                           
   Operating income                                 6,389     7,815
                                                           
Interest income                                       327       351
Interest expense                                      (48)      (81)
Other income/(expense)                               (369)       31
                                                  -------   -------
                                                           
Income before income taxes                          6,299     8,116
                                                           
Income taxes                                       (2,493)   (3,251)
                                                  -------   -------
                                                           
   Net income                                     $ 3,806     4,865
                                                  =======   =======
                                                           
Earnings per Common share                                  
 Basic                                            $   .25       .38
                                                  =======   =======
 Assuming dilution                                $   .25       .38
                                                  =======   =======
                                                           
Dividends declared per Common share               $ .0625     .0625
                                                  =======   =======
                                                           
Average Common shares outstanding (thousands)      12,806    12,798
                                                  =======   =======
 


See accompanying notes to consolidated financial statements.

                                       4
<PAGE>
 
                           DELTIC TIMBER CORPORATION
                               AND SUBSIDIARIES
               Consolidated Statements of Cash Flows (Unaudited)
                         Three Months Ended March 31,
         ------------------------------------------------------------
                            (Thousands of dollars)
 
                                                           1998      1997
                                                       --------  --------
                                                      
Operating activities                                  
 Net income                                            $  3,806     4,865
 Adjustments to reconcile above income to             
  net cash provided by operating activities          
   Depreciation, amortization, and cost of            
    fee timber harvested                                  1,729     1,260
   Deferred income taxes                                    (63)      (27)
   Gains from sales of assets                               (11)      (30)
   Real estate costs recovered upon sale                    954       819
   Equity in loss of Del-Tin Fiber, L.L.C.                  404         -
   Decrease in operating working capital              
    other than cash and cash equivalents                  2,325     1,513
   Other                                                   (226)      279
                                                       --------  --------
       Net cash provided by operating activities          8,918     8,679
                                                       --------  --------
                                                      
Investing activities                                  
 Capital expenditures requiring cash                     (9,789)   (4,910)
 Net change in purchased stumpage inventory              (3,731)   (4,139)
 Proceeds from sales of assets                               18        51
 Investment in and advances to Del-Tin Fiber,         
  L.L.C. - net                                               67    (3,000)
 Other - net                                                130        13
                                                       --------  --------
       Net cash required by investing activities        (13,305)  (11,985)
                                                       --------  --------
                                                      
Financing activities                                  
 Repayments of long-term debt                            (1,984)   (1,738)
 Bank overdraft                                             153         -
 Preferred Stock dividends paid                            (566)        -
 Common Stock dividends paid                               (801)     (800)
                                                       --------  --------
       Net cash required by financing activities         (3,198)   (2,538)
                                                       --------  --------
                                                      
Net decrease in cash and cash equivalents                (7,585)   (5,844)
Cash and cash equivalents at January 1                   31,045    18,162
                                                       --------  --------
                                                      
Cash and cash equivalents at March 31                  $ 23,460    12,318
                                                       ========  ========
                                                      
Supplemental disclosures                              
 Income taxes paid, net of refunds                     $    309       239
                                                       ========  ========
                                                      
 Interest paid, net of amounts capitalized             $    163       237
                                                       ========  ========
                                                      
 Additions to debt - owner financing                   $    347        95
                                                       ========  ========
                                                      
 Common Stock dividends declared, not paid             $      -       800
                                                       ========  ========
 

See accompanying notes to consolidated financial statements.

                                       5
<PAGE>
 
                           DELTIC TIMBER CORPORATION
                               AND SUBSIDIARIES
                Consolidated Statements of Stockholders' Equity
                -----------------------------------------------
                            (Thousands of dollars)
 
                                                       March 31,   Dec. 31,
                                                           1998       1997
                                                      ---------  ---------
                                                     (unaudited)
 
Cumulative Preferred Stock - $.01 par, authorized
 20,000,000 shares, 600,000 shares issued as
 Redeemable Preferred Stock                            $      -          -
                                                      ---------  ---------
 
Common Stock - $.01 par, authorized 50,000,000
 shares, 12,813,879 shares issued                           128        128
                                                      ---------  ---------
 
Capital in excess of par value
 Balance at beginning of year                            68,372     68,372
 Exercise of stock options                                   58          -
 Restricted stock transactions                              404          -
                                                      ---------  ---------
 Balance at end of period                                68,834     68,372
                                                      ---------  ---------
 
Retained earnings
 Balance at beginning of year                           111,496     98,208
 Net income                                               3,806     16,574
 Preferred Stock dividends accrued                         (566)       (86)
 Common Stock dividends declared                           (801)    (3,200)
                                                      ---------  ---------
 Balance at end of period                               113,935    111,496
                                                      ---------  ---------
 
Unamortized restricted stock awards
 Balance at beginning of year                                 -          -
 Stock awards, less amortization                           (396)         -
                                                      ---------  ---------
 Balance at end of period                                  (396)         -
                                                      ---------  ---------
 
Total stockholders' equity                            $ 182,501    179,996
                                                      =========  =========
 

                                       6
<PAGE>
 
                           DELTIC TIMBER CORPORATION
                               AND SUBSIDIARIES
                  Notes to Consolidated Financial Statements
                                March 31, 1998
                  ------------------------------------------
                                  (Unaudited)


NOTE 1 - INTERIM FINANCIAL STATEMENTS

 The interim financial information included herein is unaudited; however, such
 information reflects all adjustments which are, in the opinion of management,
 necessary for a fair presentation of the Company's financial position, results
 of operations, and cash flows for the interim periods.  All such adjustments
 are of a normal, recurring nature.  The financial statements in Deltic's 1997
 annual report on Form 10-K include a summary of significant accounting policies
 of the Company and should be read in conjunction with this Form 10-Q.  Certain
 prior period amounts have been reclassified to conform with 1998 presentation
 format.


NOTE 2 - EARNINGS PER COMMON SHARE

 The amounts used in computing earnings per share under the provisions of
 SFAS 128 consisted of the following:

                                                          Three Months Ended
                                                              March 31,
                                                          ------------------
   (Thousands of dollars)                                    1998      1997
                                                           ------    ------
   Net income                                              $3,806     4,865
   Less Preferred dividends                                  (566)        -
                                                           ------    ------
        Income available to Common shareholders            $3,240     4,865
                                                           ======    ======
                                                           
   Weighted average number of Common shares                
     used in basic EPS                                     12,806    12,798
   Effect of dilutive securities                           
     Stock options                                             27        19  
                                                           ------    ------
        Weighted average number of Common shares                
          and dilutive potential Common Stock used in           
          EPS assuming dilution                            12,833    12,817
                                                           ======    ======
                                                                  
   Earnings per Common share                                      
     Basic                                                 $  .25       .38
                                                           ======    ======
     Assuming dilution                                     $  .25       .38
                                                           ======    ======


NOTE 3 - INVENTORIES

 Inventories at the balance sheet dates consisted of the following:


                                                           Mar. 31,  Dec. 31,
                                                              1998      1997
                                                          --------  --------
   (Thousands of dollars)
   Logs                                                     $1,989     3,278
   Finished products                                         4,652     5,058
   Materials and supplies                                      295       259
                                                            ------    ------
                                                            $6,936     8,595
                                                            ======    ======

                                       7
<PAGE>
 
                           DELTIC TIMBER CORPORATION
                               AND SUBSIDIARIES
                  Notes to Consolidated Financial Statements
                                March 31, 1998
                  ------------------------------------------
                                  (Unaudited)


NOTE 4 - INVESTMENT IN DEL-TIN FIBER, L.L.C.

 Deltic recorded its 50-percent equity in the $808,000 of start-up costs
 recorded to-date by Del-Tin Fiber, L.L.C., a development stage company, during
 the three months ended March 31, 1998.  Such amount, $404,000 net to Deltic,
 has been included in Other Income/Expense on the Consolidated Statement of
 Income.


NOTE 5 - TIMBER AND TIMBERLANDS

 Timber and timberlands at the balance sheet dates consisted of the following:
 
                                                      Mar. 31,   Dec. 31,
                                                         1998       1997
                                                     --------   --------
 
   (Thousands of dollars)
   Purchased stumpage inventory                      $ 14,276     10,545
   Timberlands                                         45,101     44,846
   Fee timber                                          86,974     80,534
   Logging facilities                                   1,597      1,592
                                                     --------   --------
                                                      147,948    137,517
   Less accumulated costs of fee timber harvested
     and facilities depreciation                      (29,907)   (29,311)
                                                     --------   --------
                                                     $118,041    108,206
                                                     ========   ========
 

NOTE 6 - PROPERTY, PLANT, AND EQUIPMENT

 Property, plant, and equipment at the balance sheet dates consisted of the
following:
 
                                                      Mar. 31,   Dec. 31,
                                                         1998       1997
                                                     --------   --------
   (Thousands of dollars)
   Land and land improvements                        $  7,450      7,452
   Buildings and structures                             7,973      7,966
   Machinery and equipment                             60,103     58,138
                                                     --------   --------
                                                       75,526     73,556
   Less accumulated depreciation                      (34,785)   (33,910)
                                                     --------   --------
                                                     $ 40,741     39,646
                                                     ========   ========
 

                                       8
<PAGE>
 
                           DELTIC TIMBER CORPORATION
                               AND SUBSIDIARIES
                  Notes to Consolidated Financial Statements
                                March 31, 1998
                  ------------------------------------------
                                  (Unaudited)


NOTE 7 - BUSINESS SEGMENTS

 In June 1997, the Financial Accounting Standards Board issued SFAS 131,
 Disclosures about Segments of an Enterprise and Related Information.  SFAS 131
 supersedes and/or amends the business segment disclosures required under
 various preceding pronouncements, effective for fiscal year beginning after
 December 15, 1997, with earlier application encouraged.  This new standard
 defines additional information to be disclosed for each reportable segment and
 requires that each operating segment for which an enterprise's chief operating
 decision maker regularly assesses performance be disclosed as a reportable
 segment.

 As a result, the Company divided its previous Forest Products segment into two
 separate reporting segments, Woodlands and Mills.  Deltic also elected to adopt
 SFAS 131 effective for the first quarter of 1998.  All 1997 business segment
 information has been restated for comparative purposes.

 Information about the Company's business segments consisted of the following:
 
 
                                                     Three Months Ended  
                                                          March 31,
                                                     -------------------
(Thousands of dollars)                                   1998       1997
                                                     --------   --------
 Net sales
   Woodlands                                          $ 9,026      7,237
   Mills                                               17,007     15,965
   Real Estate                                          2,413      2,579
   Agriculture                                            463      1,103
   Eliminations*                                       (1,901)    (2,520)
                                                     --------   --------
                                                      $27,008     24,364
                                                     ========   ========
 
 Income before income taxes
   Woodlands                                          $ 7,786      6,168
   Mills                                                 (164)     1,325
   Real Estate                                            229      1,285
   Agriculture                                             55        498
   Corporate                                           (1,581)    (1,461)
   Eliminations                                            64          -
                                                     --------   --------
     Operating income                                   6,389      7,815
   Interest income                                        327        351
   Interest expense                                       (48)       (81)
   Other income/(expense)                                (369)        31
                                                     --------   --------
                                                      $ 6,299      8,116
                                                     ========   ========
 

 *Intersegment sales of pine sawtimber from Woodlands to Mills

                                       9
<PAGE>
 
                           DELTIC TIMBER CORPORATION
                               AND SUBSIDIARIES
                  Notes to Consolidated Financial Statements
                                March 31, 1998
                  ------------------------------------------
                                  (Unaudited)
 
                                                    Three Months Ended
                                                        March 31,
                                                    ------------------
   (Thousands of dollars)                             1998        1997
                                                    ------      ------
Depreciation, amortization, and
 cost of fee timber harvested   
   Woodlands                                       $   629         525
   Mills                                               821         545
   Real Estate                                          97          62
   Agriculture                                         125         119
   Corporate                                            57           9
                                                   -------     -------
                                                   $ 1,729       1,260
                                                   =======     =======
                                                             
Capital expenditures                                         
   Woodlands                                       $ 6,815       3,633
   Mills                                             1,964         516
   Real Estate                                       1,269         569
   Agriculture                                          65         105
   Corporate                                            23          87
                                                   -------     -------
                                                   $10,136       4,910
                                                   =======     =======
                                                                    
                                       10                         
                                                                  
                                                                  
                                                                  
                                                                  
                                                                  
                                                                 
                                                                 
                                                                  
                                                                  
                                                                  
                                                                  
                                                                  
                                                                  
                                                                  
                                                                  
<PAGE>
 
ITEM 2.   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
          RESULTS OF OPERATIONS


RESULTS OF OPERATIONS


     Net income for the first quarter of 1998 was $3.8 million, $.25 a share, a
decrease of 22 percent when compared to first quarter of 1997 net income of $4.9
million, $.38 a share. Net cash provided by operating activities was $8.9
million, an increase of $.2 million from a year ago.

     In the current quarter, operating income decreased $1.4 million.  The
Woodlands segment increased $1.6 million due primarily to a 15-percent increase
in the pine sawtimber harvest level and an eight-percent increase in the average
price for pine sawtimber sold.  The Company's Mills segment decreased $1.5
million mainly as a result of a six-percent decrease in finished lumber average
sales price combined with a ten-percent increase in the average manufacturing
cost per thousand board feet sold.  Real Estate operations decreased $1.1
million due primarily to the sale of a 13-acre commercial tract in the first
quarter of 1997.  Agriculture segment results decreased $.4 million primarily as
the result of the timing of product sales.

     Woodlands segment generated net sales of $9 million in the current quarter
compared to $7.2 million a year ago. Sales of pine sawtimber increased $1.6
million as the result of a 2.5 million board feet - Doyle scale ("MMBF-DS")
increase in the pine sawtimber harvest level to 18.8 MMBF-DS and a $33 per
thousand board feet - Doyle scale ("MBF-DS") increase in average sales price to
$440 per MBF-DS. Operating income was $7.8 million in 1998 compared to $6.2
million in 1997, a 26-percent increase, primarily the result of the increased
sales of pine sawtimber.

     The Company's Mills segment operations recorded net sales of $17 million in
the first quarter of 1998 compared to $16 million in the first quarter of 1997.
The current period included a $.5 million settlement of the business
interruption claim filed as a result of a fire at the Ola Mill during 1997.
Finished lumber sales increased $.4 million due to an eight-percent increase in
sales volume to 39.8 million board feet, partially offset by a $20 per thousand
board feet ("MBF") drop in sales price from $380 per MBF a year ago.  Operating
loss in the first quarter of 1998 was $.2 million compared to operating income
in the first quarter of 1997 of $1.3 million due primarily to a $34 per MBF
increase in lumber manufacturing cost, primarily the result of increased log
cost.

     Real Estate segment net sales totaled $2.4 million in the current quarter
compared to $2.6 million a year ago. A 13-acre commercial tract was sold in 1997
for $100,000 per acre, while no commercial development acreage was sold during
1998. Residential lot sales at Chenal Valley increased by 22 lots to 40;
however, the average sales price decreased from $62,600 to $40,500 per lot, a
decrease of 36 percent. Operating income was $.2 million in the first quarter of
1998 compared to $1.3 million during the first quarter of 1997 as the result of
the decreased margin from commercial development sales.

     Agriculture operations recorded net sales of $.5 million for the first
three months of 1998 compared to $1.1 million during the first three months of
1997 and operating income was $.1 million in the current quarter and $.5 million
a year ago due primarily to the timing of product sales.

     The Company recorded its equity in the start-up costs incurred to-date by
Del-Tin Fiber, L.L.C., reported in "Other income/(expense)",  in the amount of
$.4 million during the current period. Income tax expense decreased to $2.5
million for the first quarter of 1998 from $3.3 million in the first quarter of
1997 due to lower pretax earnings.

                                       11
<PAGE>
 
FINANCIAL CONDITION


     During the first quarter of 1998, net cash provided by operating activities
totaled $8.9 million compared to $8.7 million during the first quarter of 1997.
Changes in operating working capital, other than cash and cash equivalents,
provided cash of $1.4 million for this first three months of 1998 and $1.5
million for the 1997 period.

     Capital expenditures required cash of $9.8 in the current quarter and $4.9
million a year ago. The increase was due primarily to $6.6 million utilized to
acquire timberland acreage.  Total capital expenditures are summarized by
segment in the following table.

 
                  -------------------------------------------
                                               Three Months
                                              Ended March 31,
                  -------------------------------------------
                  (Thousands of dollars)         1998   1997
                  -------------------------------------------
                  Woodlands                   $ 6,815  3,633
                  Mills                         1,964    516
                  Real Estate                   1,269    569
                  Agriculture                      65    105
                  Corporate                        23     87
                  -------------------------------------------
                   Capital expenditures       $10,136  4,910
                  ===========================================

     The net change in purchased stumpage inventory required cash of $3.7
million in the first quarter of 1998 and $4.1 million a year ago.  During the
current quarter, the Company paid dividends of $1.4 million, $.8 million for
Common Stock and $.6 million for Redeemable Preferred Stock, compared to $.8
million for Common Stock in the 1997 period.  Repayments of debt utilized $2
million.  These net uses of funds were the primary factors in the $7.7 million
reduction in working capital from $38 million at December 31, 1997.  However,
the Company believes that the amounts available from its Redeemable Preferred
Stock issuance, operating cash flows, funds available under its credit
facilities, and future debt or equity financings will be sufficient to meet its
expected cash needs and planned capital expenditures for the foreseeable future.

                                       12
<PAGE>
 
                          PART II - OTHER INFORMATION



ITEM 1.   LEGAL PROCEEDINGS

          From time to time, the Company is involved in litigation incidental to
  its business. Currently, there are no material legal proceedings.



ITEM 2.   CHANGES IN SECURITIES

          None.


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

               27    Financial Data Schedule.

          (b)  Reports on Form 8-K

               None.

                                       13
<PAGE>
 
                                  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.


DELTIC TIMBER CORPORATION



By:        /s/Ron L. Pearce                         Date:      May 8, 1998
   ------------------------------------                  -----------------------
         Ron L. Pearce, President
       (Principal Executive Officer)



         /s/Clefton D. Vaughan                      Date:      May 8, 1998
---------------------------------------                  -----------------------
    Clefton D. Vaughan, Vice President,
        Finance and Administration
       (Principal Financial Officer)



           /s/Emily R. Evers                        Date:      May 8, 1998
---------------------------------------                  -----------------------
        Emily R. Evers, Controller
      (Principal Accounting Officer)

                                       14