<PAGE>   1

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549

                                    FORM 10-Q

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

For Quarterly Period Ended  March 31, 1998         Commission file number 1-7088
                          ------------------                             -------


                        AMERICAN BUSINESS PRODUCTS, INC.
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

        Georgia                                            58-1030529
--------------------------------------------------------------------------------
(State of Incorporation)                       (IRS Employer Identification No.)

2100 RiverEdge Parkway, Suite 1200, Atlanta, Georgia                    30328
--------------------------------------------------------------------------------
(Address of principal executive offices)                              (Zip Code)

Registrant's telephone number, including area code                (770) 953-8300
                                                                  --------------

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
   -----    -----


  Common Stock, $2.00 par value                         16,148,445 shares
  -----------------------------                         -----------------
             (Class)                             (Outstanding at March 31, 1998)

                                  Page 1 of 10
                            Exhibit Index on Page 10


<PAGE>   2

                         Part I -- FINANCIAL INFORMATION

Item 1.  Financial Statements

                        AMERICAN BUSINESS PRODUCTS, INC.
                    CONDENSED CONSOLIDATED INCOME STATEMENTS
         FOR THE THREE MONTHS ENDED MARCH 31, 1998 AND 1997 (UNAUDITED)
                  (Dollars in thousands except per share data)

<TABLE>
<CAPTION>
                                                       1998                1997
                                                   ------------        ------------
<S>                                                <C>                 <C>         
NET SALES                                          $    132,993        $    127,048
                                                   ------------        ------------

COST AND EXPENSES
 Cost of goods sold                                      93,500              89,807
 Selling and administrative expenses                     30,335              28,403
                                                   ------------        ------------
                                                        123,835             118,210
                                                   ------------        ------------

OPERATING INCOME                                          9,158               8,838

OTHER INCOME (EXPENSE)
 Interest expense                                        (1,155)             (1,725)
 Interest income                                          1,088                 984
 Miscellaneous - net                                        308               3,722
                                                   ------------        ------------
                                                            241               2,981
                                                   ------------        ------------

INCOME BEFORE INCOME TAXES                                9,399              11,819

PROVISION FOR INCOME TAXES                                3,453               4,444
                                                   ------------        ------------

NET INCOME                                         $      5,946        $      7,375
                                                   ============        ============

EARNINGS PER COMMON SHARE - BASIC                  $       0.37        $       0.45

EARNINGS PER COMMON SHARE - DILUTED                $       0.36        $       0.45

DIVIDENDS PER COMMON SHARE                         $      0.155        $      0.155

WEIGHTED AVERAGE NUMBER OF
 COMMON SHARES OUTSTANDING                           16,286,548          16,408,622

WEIGHTED AVERAGE NUMBER OF COMMON AND
 COMMON EQUIVALENT SHARES OUTSTANDING                16,383,622          16,533,040
</TABLE>

     See accompanying notes to condensed consolidated financial statements.




                                       2
<PAGE>   3

                        AMERICAN BUSINESS PRODUCTS, INC.
                      CONDENSED CONSOLIDATED BALANCE SHEETS
                             (Dollars in thousands)

<TABLE>
<CAPTION>
                                                        March 31,    December 31,
                                                          1998           1997
                                                      ------------   ------------
                                                       (Unaudited)
<S>                                                   <C>            <C>     
CURRENT ASSETS
 Cash and cash equivalents                              $ 68,879       $ 75,092
 Accounts receivable, less allowances of
  $2,383 and $2,121                                       62,234         58,522
 Inventories                                              33,303         32,314
 Other                                                     4,459          9,987
                                                        --------       --------
  Total Current Assets                                   168,875        175,915

PROPERTY, PLANT AND EQUIPMENT - AT COST
 Land                                                      2,954          2,954
 Buildings and improvements                               43,909         43,807
 Machinery, equipment and software                       111,109        108,665
 Construction in progress                                 12,806          8,597
                                                        --------       --------
                                                         170,778        164,023
 Less accumulated depreciation                            78,372         75,065
                                                        --------       --------
                                                          92,406         88,958

INTANGIBLE ASSETS FROM ACQUISITIONS
 Goodwill, less amortization of $5,194 and $4,970         27,008         27,232
 Other, less amortization of $5,049 and $4,957               898            990
                                                        --------       --------
                                                          27,906         28,222

DEFERRED INCOME TAXES                                     14,184         13,945
OTHER ASSETS                                              22,183         25,740
                                                        --------       --------
TOTAL ASSETS                                            $325,554       $332,780
                                                        ========       ========

CURRENT LIABILITIES
 Accounts payable                                       $ 46,136       $ 48,811
 Salaries and wages                                        7,643          7,789
 Profit sharing contributions                                967          2,730
 Current maturities of long-term debt                     12,047         12,047
                                                        --------       --------
  Total Current Liabilities                               66,793         71,377

LONG-TERM DEBT                                            42,746         42,850
SUPPLEMENTAL RETIREMENT BENEFITS                          19,805         19,869
POSTRETIREMENT AND POSTEMPLOYMENT BENEFITS                16,853         16,987

STOCKHOLDERS' EQUITY
 Common stock - $2 par value; authorized 50,000,000
  shares, issued 16,702,847 and 16,676,932 shares         33,406         33,354
 Additional paid-in capital                                7,321          7,144
 Retained earnings                                       148,503        145,062
 Foreign currency translation adjustment                     261            261
                                                        --------       --------
                                                         189,491        185,821
 Less 554,402 and 261,659 shares of common
  stock in treasury - at cost                             10,134          4,124
                                                        --------       --------
                                                         179,357        181,697
                                                        --------       --------
TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY              $325,554       $332,780
                                                        ========       ========
</TABLE>

     See accompanying notes to condensed consolidated financial statements.




                                       3
<PAGE>   4

                        AMERICAN BUSINESS PRODUCTS, INC.
                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
         FOR THE THREE MONTHS ENDED MARCH 31, 1998 AND 1997 (UNAUDITED)
                             (Dollars in thousands)

<TABLE>
<CAPTION>
                                                                    1998            1997
                                                                ------------    ------------
<S>                                                             <C>             <C>     
CASH FLOWS FROM OPERATING ACTIVITIES
 Net income                                                       $  5,946        $  7,375
 Adjustments to reconcile net income to net cash
  provided by operating activities:
    Depreciation and amortization                                    3,724           3,328
    Gain on disposition of plant and equipment                          (1)         (2,423)
    Amortization of discount                                            --            (612)
    Change in assets and liabilities:
    (Increase) decrease in accounts receivable                      (3,712)            524
    (Increase) decrease in inventories                                (989)          2,424
    Decrease in other current assets                                 5,528           1,514
    Increase in intangible and other assets                           (115)            (32)
    Decrease in accounts payable                                    (2,675)         (7,989)
    Decrease in other current liabilities                           (1,909)         (6,575)
    Increase (decrease) in supplemental retirement benefits
     and postemployment benefits                                      (198)            249
    (Increase) decrease in deferred income taxes                      (239)             26
                                                                  --------        --------

          Total adjustments                                           (586)         (9,566)

          Net cash provided (used) by operating activities           5,360          (2,191)


CASH FLOWS FROM INVESTING ACTIVITIES
 Purchase of short-term investment                                      --         (47,207)
 Decrease in and liquidation of cash value of life insurance         3,744           2,282
 Additions to plant and equipment                                   (6,973)         (8,872)
 Proceeds from disposition of plant and equipment                       46           4,504
                                                                  --------        --------
   Net cash used in investing activities                            (3,183)        (49,293)


CASH FLOWS FROM FINANCING ACTIVITIES
 Reductions of long-term debt                                         (104)           (156)
 Sales and exchanges of common stock                                   207              91
 Repurchase of common stock                                         (5,988)             --
 Dividends paid                                                     (2,505)         (2,543)
                                                                  --------        --------
   Net cash used by financing activities                            (8,390)         (2,608)


Net decrease in cash and cash equivalents                           (6,213)        (54,092)
Cash and cash equivalents at beginning of period                    75,092          82,516
                                                                  --------        --------
Cash and cash equivalents at end of period                        $ 68,879        $ 28,424
                                                                  ========        ========
</TABLE>


     See accompanying notes to condensed consolidated financial statements.




                                       4
<PAGE>   5

                        AMERICAN BUSINESS PRODUCTS, INC.

              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS

1.       Unaudited Condensed Consolidated Financial Statements

The condensed consolidated financial statements have been prepared in accordance
with generally accepted accounting principles which in certain instances require
the use of management's estimates. The information contained in these condensed
consolidated financial statements and notes for the three month periods ended
March 31, 1998 and 1997 is unaudited but, in the opinion of management, all
adjustments necessary for a fair presentation of such information have been
made. All such adjustments are of a normal recurring nature. Certain information
and footnote disclosures normally included in financial statements prepared in
accordance with generally accepted accounting principles have been omitted
pursuant to applicable rules and regulations of the Securities and Exchange
Commission. The condensed consolidated financial statements included herein
should be read in conjunction with the audited financial statements and notes
thereto contained in the Company's Annual Report on Form 10-K for the year ended
December 31, 1997.

2.       Consolidation Policy

The condensed consolidated financial statements include the accounts of the
Company and its subsidiaries, all of which are wholly-owned. Intercompany
balances and transactions have been eliminated.

3.       Nature of Operations

The Company markets envelope products, business forms, labels and other supplies
for business and industry and, except for business forms, manufactures such
supplies, manufactures and distributes hardcover and softcover books for the
publishing industry; and provides extrusion coating and laminating of papers,
films, and nonwoven fabrics for use in medical, industrial and consumer
packaging. The markets for these products are located principally throughout the
continental United States.

4.       Net Income Per Share

Net income per common share is based upon the weighted average number of common
and common equivalent shares outstanding during the respective periods. The only
common equivalent shares are those related to stock options outstanding during
the respective periods.

5.       New Accounting Standard

In February 1998, the Financial Accounting Standards Board ("FASB") issued
Statement of Financial Accounting Standards No. 132, "Employers' Disclosure
about Pensions and Other Postretirement Benefits" ("SFAS No. 132"). This
statement revises employers' disclosures about pensions and other postretirement
benefit plans but does not change the measurement or recognition of those plans.
It standardizes the disclosure requirements to the extent practicable, requires
additional information on changes in the benefit obligations and fair values of
plan assets that will facilitate financial analysis and eliminates certain
disclosures that are no longer as useful as they were when FASB Statements No.
87, Employers' Accounting for Pensions, No. 88, Employers' Accounting for
settlements and Curtailments of Defined Benefit Pension Plans and for
Termination Benefits, and No. 106, Employers' Accounting for Postretirement
Benefits Other Than Pensions, were issued. This statement is effective for
fiscal years beginning after December 15, 1997.

In March 1998, the American Institute of Certified Public Accountants ("AICPA"),
issued Statement of Position 98-1, "Accounting for the Costs of Computer
Software Developed or Obtained for Internal Use" ("SOP 98-1"). This statement is
effective for financial statements for fiscal years beginning after December 15,
1998. Earlier application is encouraged in fiscal years for which annual
financial statements have not been issued. The Company implemented SOP 98-1 in
the first quarter of 1998. SOP 98-1 will not have a material impact on the
Company's financial condition or results of operations.




                                       5
<PAGE>   6

6.       Inventories ($000's)

         Inventories consisted of the following at the dates indicated:

<TABLE>
<CAPTION>
                                                March 31,   December 31,
                                                  1998          1997    
                                                ---------   ------------
         <S>                                    <C>         <C>    
         Products finished or in process         $17,353       $16,076
         Raw materials                            15,728        15,628
         Supplies                                    222           610
                                                 -------       -------
                                                 $33,303       $32,314
                                                 =======       =======
</TABLE>

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

Results of Operations

Net sales for the first quarter of 1998 were $132,933,000, a 4.6% increase from
the $127,048,000 for the first quarter of 1997. The increased sales resulted
from revenue gains at the Company's largest business supplies subsidiary, Curtis
1000 Inc. ("Curtis") and at the Company's custom label, extrusion coating and
envelope manufacturing subsidiaries, partially offset by declines at the book
printing subsidiary.

The Company's gross margin percent was 29.7% for the first quarter of 1998
compared to 29.3% for the first quarter of 1997. The increased margin in 1998 is
primarily due to the reorganization of Curtis into five regional profit centers
which has moved decision making closer to customers, the salesforce and the shop
floor as well as progress implementing key components of a profit improvement
plan at Curtis.

Selling and administrative expense for the first quarter of 1998 was
$30,335,000, an increase of 6.8% from the $28,403,000 for the first quarter of
1997. Included in the results for 1998 were charges related to management
changes at Curtis of $1,415,000. Excluding these charges, selling and
administrative expense would have been $28,920,000.

Interest expense for the first quarter of 1998 was $1,155,000, a decrease of
33.0% from the $1,725,000 for the first quarter of 1997. The decrease resulted
primarily from a lower interest rate applied to certain loans secured by Company
owned life insurance policies as well as reduced long term debt.

Interest income for the first quarter of 1998 was $1,088,000, an increase of
10.6% from the $984,000 for the first quarter of 1997. The increase resulted
primarily from improved returns due to centralizing and automating the Company's
cash management systems.

Miscellaneous net for the first quarter of 1998 was $308,000, a decrease of
91.7% from the $3,722,000 for the first quarter of 1997. Included in the 1997
results were gains of $2,325,000 on disposal of realty rendered redundant to
operating needs by the Company's now completed plant consolidation program.
Excluding the realty gains, miscellaneous net would have been $1,397,000, which
primarily was comprised of unusually high Company owned life insurance policy
death benefits received in the first quarter of 1997.

The Company's effective tax rate was 36.7% and 37.6% for the first quarter of
1998 and first quarter of 1997, respectively. The decrease in 1998 resulted
primarily from recognition of the benefit of tax strategies developed by the
Company.




                                       6
<PAGE>   7

Pro Forma Financial Information

The 1998 results include charges of $834,000 after tax, or $0.05 per share,
related to management changes at Curtis. Without the charges, the Company would
have shown net income of $6,780,000, or $0.42 per share.

The 1997 results include gains of $1,395,000 after tax on the disposal of
redundant realty. Without the realty gains, the Company would have shown net
income of $5,980,000, or $0.36 per share.

Financial Condition

Stockholders' equity decreased $2,340,000 during the first quarter of 1998 due
primarily to share repurchases by the Company and totaled $179,357,000 at March
31, 1998.

Cash and cash equivalents decreased $6,213,000 during the first quarter of 1998
and totaled $68,879,000 at March 31, 1998. Operating activities provided
$5,360,000 in cash during the first three months of 1998. Cash was used to
purchase $6,973,000 of property, plant and equipment, reduce long-term debt by
$104,000, repurchase $5,988,000 of common stock and pay $2,505,000 in dividends.

The Company maintains a revolving credit agreement (the "Credit Agreement") with
a bank providing for loans up to $50,000,000 at interest rates related to prime
and Eurocurrency rates. At March 31, 1998 there were no borrowings under the
Credit Agreement. Curtis has borrowed $6,460,000 through a variable interest
rate industrial revenue bond (the "Bond") due May 1, 2031. The interest rate on
the Bond was 3.80% at March 31, 1998. The Bond is supported by a letter of
credit issued pursuant to the Credit Agreement which commensurately reduces the
balance available to the Company under the Credit Agreement.

The Company believes its liquid current assets, internal cash flow, availability
of additional borrowing under its existing loan agreements, and to the extent
necessary, additional external financing, should adequately meet the Company's
needs for the foreseeable future.

In December 1997 the Company announced plans to purchase up to 1.7 million
shares or approximately 10% of its outstanding Common Stock through negotiated
transactions and open market purchases. As of March 31, 1998, the Company had
acquired 318,000 shares at a cost of approximately $6,554,000.

Risks and Uncertainties

The Company has reviewed all significant financial and manufacturing systems to
determine compliance with the Year 2000 and has developed a plan of action
intended to correct or replace those systems not in compliance. The cost
associated with correcting systems not in compliance has not been determined,
although based on preliminary management estimates the Company does not believe
these costs will have a material impact on the Company's financial position. The
Company plans to have all corrective action necessary completed by June 30,
1999. Costs associated with correcting existing systems will be expensed as
incurred. Costs associated with replacing older systems with better, modern
systems, which will be Year 2000 complaint, will be capitalized and amortized
based on Company policy. The Company also conducts business electronically with
certain external partners, including suppliers, customers and financial service
organizations. The Company is currently contacting external parties with which
it interacts to determine any Year 2000 compliance issues. Failure to
successfully execute the Company's Year 2000 compliance plans or the failure of
external parties to achieve Year 2000 compliance could have a material adverse
impact on the Company's financial position and results of operations.

Except for historical information contained herein, the matters set forth in
this report including but not limited to statements regarding the Company's
expectations, hopes, intentions or strategies regarding the future, are forward
looking statements that involve certain risks and uncertainties that could cause
actual results to differ materially from those in the forward looking
statements. The Company assumes no obligation to update any such forward looking
statements. The Company's expectations respecting future sales and profits
assume, among other things, reasonable continued growth in the general economy
which affects demand for the Company's products. Future profits may vary from
the Company's expectations due to factors such as possible future adjustments to
the Company's profit improvement plans, particularly at Curtis 1000 Inc., as the
effects of implementing these plans are realized. The costs and benefits of the
Company's plant consolidation and order processing redesign programs may 




                                       7
<PAGE>   8

vary from the Company's expectations due to factors such as: the extent of
management's ability to control and ultimately eliminate duplication of costs,
inefficiencies, overheads, and operating bottlenecks associated with
transferring production from closing to continuing plants; the extent of the
Company's ability to complete the development and implementation of order entry
automation programs within expected time and cost constraints; and the
difficulties inherent in forecasting the operating results of an operating mode
different from that which exists at the time the forecast is made. Although the
Company believes its plan to achieve timely Year 2000 compliance is reasonable
based on known facts and circumstances it remains possible that, dependent on
future events such as availability in the labor force of information systems
programmers and other information systems personnel, responsiveness of third
parties beyond the Company's control such as system vendors, service suppliers,
and others with whom the Company interacts and the capabilities of the
information systems which the Company intends to utilize, achieving Year 2000
compliance may take longer or cost more than the Company presently anticipates.

Accounting Standards

In February 1998, The Financial Accounting Standards Board ("FASB") issued
Statement of Financial Accounting Standards No. 132, "Employers' Disclosure
about Pensions and Other Postretirement Benefits" ("SFAS No. 132"). This
statement revises employers' disclosures about pensions and other postretirement
benefit plans but does not change the measurement or recognition of those plans.
It standardizes the disclosure requirements to the extent practicable, requires
additional information on changes in the benefit obligations and fair values of
plan assets that will facilitate financial analysis and eliminates certain
disclosures that are no longer as useful as they were when FASB Statements No.
87, Employers' Accounting for Pensions, No. 88, Employers' Accounting for
settlements and Curtailments of Defined Benefit Pension Plans and for
Termination Benefits, and No. 106, Employers' Accounting for Postretirement
Benefits Other Than Pensions, were issued. This statement is effective for
fiscal years beginning after December 15, 1997.

In March 1998, the American Institute of Certified Public Accountants ("AICPA"),
issued Statement of Position 98-1, "Accounting for the Costs of Computer
Software Developed or Obtained for Internal Use" ("SOP 98-1"). This statement is
effective for financial statements for fiscal years beginning after December 15,
1998. Earlier application is encouraged in fiscal years for which annual
financial statements have not been issued. The Company implemented SOP 98-1 in
the first quarter of 1998. SOP 98-1 will not have a material impact on the
Company's financial condition or results of operations.








                                       8
<PAGE>   9



                           PART II - OTHER INFORMATION

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

a.       Exhibits attached hereto:

NUMBER                              DESCRIPTION

  27           Financial Data Schedules for First Quarter 1998 10-Q (for SEC use
               only)

b.       Reports on Form 8-K.

               On February 24, 1998, the Company filed a Current Report on Form
               8-K to report that Larry L. Gellerstedt, III had been elected
               President and Chief Executive Officer, effective March 30, 1998.

                                   SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                        AMERICAN BUSINESS PRODUCTS, INC.
                                                  (Registrant)

         Date:  April 22, 1998                 /s/ Richard G. Smith
                                             -----------------------------------
                                             Richard G. Smith
                                             Vice President
                                             and Chief Financial Officer



                                               /s/ Raymond J. Wilson
                                             -----------------------------------
                                             Raymond J. Wilson
                                             Corporate Controller






                                       9
<PAGE>   10



                        AMERICAN BUSINESS PRODUCTS, INC.

                                INDEX OF EXHIBITS


NUMBER                              DESCRIPTION

27                  Financial Data Schedules for First Quarter 1998 10-Q
                    (for SEC use only)








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