<PAGE>   1


                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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



For The Quarter Ended            September 30, 1998
--------------------------------------------------------------------------------


Commission file number                0-7024
--------------------------------------------------------------------------------


                              THE FIRST YEARS INC.
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)


Massachusetts                                       04-2149581
--------------------------------------------------------------------------------
(State or other jurisdiction of                  (I.R.S. Employer 
incorporation or organization)                   Identification No.)



                One Kiddie Drive, Avon, Massachusetts 02322-1171
--------------------------------------------------------------------------------
                    (Address of principal executive offices)
                                   (Zip Code)


                                 (508) 588-1220
--------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)



--------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                          if changed since last report)


Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

Yes  X   No  
    ---     ---

The number of shares of Registrant's common stock outstanding on October 31,
1998 was 10,415,012.


<PAGE>   2


                              THE FIRST YEARS INC.


                                      INDEX
                                      -----

PART I - FINANCIAL INFORMATION:                             Page 

Condensed Consolidated Balance Sheets                         1

Condensed Consolidated Statements of Income                   2

Condensed Consolidated Statements of Cash Flows               3

Notes to Condensed Consolidated Financial Statements          4 - 5

Management's Discussion and Analysis of Financial
  Condition and Results of Operations                         6 - 8

PART II - OTHER INFORMATION

Other information                                             9

SIGNATURES                                                    10

EXHIBIT INDEX                                                 11


<PAGE>   3


<TABLE>
<CAPTION>
                              THE FIRST YEARS INC.
                      Condensed Consolidated Balance Sheets

                     ASSETS
                                                September 30,  December 31,
                                                    1998           1997
                                                -------------  ------------
                                                (Unaudited)
<S>                                            <C>             <C>         
CURRENT ASSETS:
 Cash and cash equivalents                     $ 19,684,018    $  7,697,040
 Accounts receivable, net                        21,826,632      19,962,226
 Inventories                                     19,321,600      24,372,881
 Prepaid expenses and other assets                  433,721         414,764
 Deferred tax assets                              1,279,000       1,279,000
                                               ------------    ------------
       Total current assets                      62,544,971      53,725,911
                                               ------------    ------------

PROPERTY, PLANT, AND EQUIPMENT:
 Land                                               167,266         167,266
 Building                                         4,042,304       4,022,095
 Machinery and molds                              7,163,181       7,151,019
 Furniture and equipment                          4,523,203       3,947,144
                                               ------------    ------------
       Total                                     15,895,954      15,287,524
 Less accumulated depreciation                    9,362,970       8,441,874
                                               ------------    ------------
   Property, plant, and equipment - net           6,532,984       6,845,650
                                               ------------    ------------
TOTAL ASSETS                                   $ 69,077,955    $ 60,571,561
                                               ============    ============

        LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES:
 Accounts payable                              $  9,271,731    $ 10,004,244
 Accrued royalty expense                          2,062,546       2,051,721
 Accrued payroll expenses                         1,277,034       1,143,063
 Accrued selling expenses                         3,013,424       2,387,029
 Federal and state income taxes payable             310,200         159,600
                                               ------------    ------------
       Total current liabilities                 15,934,935      15,745,657
                                               ------------    ------------

DEFERRED TAX LIABILITY                              816,900         816,900
                                               ------------    ------------
STOCKHOLDERS' EQUITY:
 Common stock                                     1,043,641         508,800
 Paid-In capital                                  7,359,598       6,534,308
 Retained earnings                               44,232,605      37,047,709
 Less: 21,394 shares of
   treasury stock (at cost)                        (309,724)        (81,813)
                                               ------------    ------------
       Total stockholders' equity                52,326,120      44,009,004
                                               ------------    ------------

TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY     $ 69,077,955    $ 60,571,561
                                               ============    ============
</TABLE>


     See accompanying notes to condensed consolidated financial statements.

                                     Page 1

<PAGE>   4


<TABLE>
<CAPTION>
                              THE FIRST YEARS INC.

                   Condensed Consolidated Statements of Income
                                   (Unaudited)


                                  Three Months Ended       Nine Months Ended
                                     September 30,           September 30,
                                  ------------------       ------------------
                                  1998         1997         1998        1997
                                  ----         ----         ----        ----
<S>                            <C>         <C>         <C>          <C>        
NET SALES                      $32,735,238 $27,878,092 $103,219,645 $88,397,388

COST OF PRODUCTS SOLD           18,951,345  16,249,011   61,038,625  52,247,703
                               ----------- ----------- ------------ -----------

GROSS PROFIT                    13,783,893  11,629,081   42,181,020  36,149,685


SELLING, GENERAL, AND
 ADMINISTRATIVE EXPENSES         9,241,221   8,701,661   29,451,127  26,988,068
                               ----------- ----------- ------------ -----------

OPERATING INCOME                 4,542,672   2,927,420   12,729,893   9,161,617

OTHER INCOME (EXPENSES):
  Interest expense                      --        (542)        (850)    (26,241)
  Interest income                  188,259      67,025      391,588      89,091
                               ----------- ----------- ------------ -----------


INCOME BEFORE INCOME TAXES       4,730,931   2,993,903   13,120,631   9,224,467

PROVISION FOR INCOME TAXES       1,916,000   1,190,100    5,313,800   3,744,600
                               ----------- ----------- ------------ -----------

NET INCOME                     $ 2,814,931 $ 1,803,803 $  7,806,831 $ 5,479,867
                               =========== =========== ============ ===========


BASIC EARNINGS PER SHARE             $0.27       $0.18        $0.76       $0.55
                                     =====       =====        =====       =====

DILUTED EARNINGS PER SHARE           $0.26       $0.17        $0.73       $0.53
                                     =====       =====        =====       =====


CASH DIVIDENDS PAID PER SHARE        $0.00       $0.00        $0.06       $0.05
                                     =====       =====        =====       =====
</TABLE>



     See accompanying notes to condensed consolidated financial statements.

                                Page 2

<PAGE>   5

<TABLE>
<CAPTION>

                              THE FIRST YEARS INC.

             Condensed Consolidated Statements of Cash Flows for the
                  Nine Months Ended September 30, 1998 and 1997
                                   (Unaudited)

                                                                1998        1997
                                                                ----        ----
<S>                                                      <C>            <C>         
CASH FLOWS FROM OPERATING ACTIVITIES:
 Net income                                              $  7,806,831   $  5,479,867
 Adjustments to reconcile net income to net
  cash provided by (used for) operations:
    Depreciation                                            1,260,768      1,143,226
    Provision for doubtful accounts                           115,000        245,359
    Loss on disposal of equipment                             476,067             --
Increase (decrease) arising from working capital items:
    Accounts receivable                                    (1,979,406)    (1,625,806)
    Inventories                                             5,051,281     (1,202,056)
    Prepaid expenses and other assets                         (18,957)      (511,621)
    Accounts payable and accrued expenses                    (732,513)     2,682,866
    Accrued royalties                                          10,825        574,662
    Accrued payroll expense                                   133,971        195,969
    Accrued selling expenses                                  626,395        278,931
    Federal and state income taxes - net                      150,600             --
                                                         ------------   ------------
     Net cash provided by
       operating activities                                12,900,862      7,261,397
                                                         ------------   ------------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Expenditures for property, plant,
      and equipment                                        (1,424,169)    (1,293,024)
                                                         ------------   ------------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Cash Dividend                                             (621,935)      (496,747)
   Common stock issued under stock
     option plans                                             625,820        633,272
   Tax benefit of stock option compensation                   506,400        400,000
   Repayment of industrial revenue bonds                           --       (100,000)
                                                         ------------   ------------
     Net cash provided by financing 
       activities                                             510,285        436,525
                                                         ------------   ------------

INCREASE (DECREASE) IN CASH AND
  CASH EQUIVALENTS                                         11,986,978      6,404,898

CASH AND CASH EQUIVALENTS, BEGINNING
  OF PERIOD                                                 7,697,040      4,164,587
                                                         ------------   ------------

CASH AND CASH EQUIVALENTS, END OF PERIOD                 $ 19,684,018   $ 10,569,485
                                                         ============   ============

SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:
    Cash paid for:
         Interest                                        $        850   $     26,241
                                                         ============   ============
         Income taxes                                    $  4,656,800   $  3,738,100
                                                         ============   ============

SUPPLEMENTAL SCHEDULE OF NONCASH FINANCING ACTIVITIES:
    Issuance of treasury stock                           $    227,911   $         --
                                                         ============   ============
</TABLE>


     See accompanying notes to condensed consolidated financial statements.


                                     Page 3
<PAGE>   6


                              THE FIRST YEARS INC.

              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS


1.   Amounts in the accompanying balance sheet as of December 31, 1997 are
     condensed from the Company's audited balance sheet as of that date. All
     other condensed financial statements are unaudited but, in the opinion of
     the Company, contain all normal and recurring adjustments necessary to
     present fairly the financial position as of September 30, 1998, and the
     results of operations and cash flows for the periods ended September 30,
     1998 and 1997.

2.   The Company has 30,000,000 authorized shares of $.10 par value common stock
     with 10,415,012 and 10,169,182 shares issued and outstanding as of
     September 30, 1998 and December 31, 1997, respectively.

     On May 8, 1998 the Board of Directors authorized a two-for-one stock split
     effected in the form of 100% stock dividend paid to stockholders of record
     on May 29, 1998. Accordingly, all per share and stock option data presented
     in these financial statements have been restated to reflect the split. The
     par value for the new shares issued amounted to $519,020 and was
     transferred from paid-in capital. Distribution of the new shares was paid
     on June 29, 1998

     Additionally, on May 8, 1998 the Board of Directors authorized a $0.06 per
     share annual cash dividend paid on June 29, 1998 to holders of record at
     the close of business on May 29, 1998.

3.   Computation of the Earnings Per Share ("EPS") in accordance with SFAS No.
     128 are as follows:

<TABLE>
<CAPTION>
                                  Three Months Ended         Nine Months Ended
                                     September 30,              September 30,
                                  ------------------         -----------------
                                   1998        1997          1998        1997
                                   ----        ----          ----        ----
<S>                           <C>          <C>           <C>          <C>      
AVERAGE SHARES OUTSTANDING     10,391,816   10,035,606    10,306,828   9,958,262

EFFECT OF DILUTIVE SHARES         305,155      478,852       352,809     448,796
                              -----------  -----------   ----------- -----------
AVERAGE DILUTED
  SHARES OUTSTANDING           10,696,971   10,514,458    10,659,637  10,407,058
                              ===========  ===========   =========== ===========

NET INCOME                    $ 2,814,931  $ 1,803,803   $ 7,806,831 $ 5,479,867
                              ===========  ===========   =========== ===========


BASIC EARNINGS PER SHARE            $0.27        $0.18         $0.76       $0.55
                                    =====        =====         =====       =====

DILUTED EARNINGS PER SHARE          $0.26        $0.17         $0.73       $0.53
                                    =====        =====         =====       =====
</TABLE>



                                     Page 4
<PAGE>   7


                              THE FIRST YEARS INC.

          NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS (Con't)


3.   Computation of Earnings Per Share (con't)

     As of September 30, 1998, options to purchase 1,964, 20,000 and 12,000
     shares of common stock at $15 15/16, $17 3/4 and $17 per share,
     respectively were not included in the computation of diluted EPS because
     the option's exercise price was greater than the average price of the
     common shares. The options, which expire in 2008 were still outstanding at
     September 30, 1998.

     As of September 30, 1997, options to purchase 30,000 shares of common stock
     at $13 1/2 per share, were not included in the computation of diluted EPS
     because the option's exercise price was greater than the average price of
     the common shares. The options, which expire in 2007, were still
     outstanding at September 30, 1998.

4.   The results of operations for the nine month period ended September 30,
     1998 and 1997 are not necessarily indicative of the results to be expected
     for the full year.

5.   During the first nine months of 1998, the Company did not borrow against
     its unsecured line of credit totaling $10,000,000 available from a bank.
     During 1997, the Company borrowed various amounts up to $2,500,000 of which
     there was no balance outstanding as of September 30, 1997.

6.   Statements of Financial Accounting Standards ("SFAS") No. 130 "Reporting
     Comprehensive Income" became effective for the Company during the quarter
     ended March 31, 1998. Adoption of SFAS No. 130 did not have a material
     impact on the consolidated financial statements.

     The Financial Accounting Standards Board recently issued SFAS No. 131,
     "Disclosure about Segments of an Enterprise and Related Information" and
     SFAS No. 132, "Employers' Disclosure about Pensions and Other
     Postretirement Benefits." These new standards will be effective in the
     Company's fiscal year ended December 31, 1998. SFAS No. 133 "Accounting for
     Derivative Instruments and Hedging Activities" will be effective for the
     Company's fiscal year ended December 31, 2000. The Company has not
     determined the effects, if any, that these standards will have on its
     consolidated financial statements.


                                     Page 5

<PAGE>   8


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



     Statements in this Report on Form 10-Q that are not strictly historical are
     "forward-looking" statements, as defined in the Private Securities
     Litigation Reform Act of 1995. The actual results may differ from those
     projected in the forward-looking statements due to risks and uncertainties
     that exist in the Company's operations and business environment in the
     development and introduction of new products, described more fully in the
     Company's Annual Report on Form 10-K for the year ended December 31, 1997,
     and Exhibit 99 of the Annual Report on Form 10K for the year ended December
     31,1997, filed with the Securities and Exchange Commission.

     Net sales for the first nine months of 1998 were $103.2 million, an
     increase of $14.8 million or 16.8%, as compared to $88.4 million for the
     comparable period last year. The increase was due to new product
     introductions fueling expanded retail distribution in domestic markets,
     particularly in the discount, food and pharmacy channels of distribution.

     Cost of products sold for the first nine months of 1998 was $61.0 million,
     an increase of $8.8 million or 16.8%, as compared to $52.2 million for the
     comparable period last year. As a percentage of sales, cost of products
     sold in the first nine months of 1998 and 1997 remained constant at 59.1%.

     Selling, general, and administrative expenses for the first nine months of
     1998 were $29.5 million, an increase of $2.5 million or 9.1%, as compared
     to $27.0 million over such expenses for the first nine months of 1997. The
     increase resulted primarily from costs related to increased sales volume;
     payroll and payroll related costs, and product development expenses. As a
     percentage of net sales, selling, general, and administrative expenses for
     the first nine months of 1998 decreased to 28.5% from 30.5% in the
     comparable period of 1997. The decrease reflects the continued effective
     management of selling, general, and administrative costs as well as the
     timing of certain marketing expenses.

     Income tax expense as a percentage of pretax income remained consistent at
     40.5% for the first nine months of 1998 and 1997.

     Net working capital increased by $8.6 million in the first nine months
     mainly due to profitable operations. Accounts receivable increased by $1.8
     million as a result of increased sales and inventories decreased by $5.1
     due to normal business fluctuations as well as the continued effective
     management of inventory. Cash increased by $12.0 million primarily
     resulting from funds generated from operations and the decrease in
     inventories.


                                     Page 6

<PAGE>   9


         Management's Discussion and Analysis of Financial Condition and
                          Results of Operations (Con't)



     The Company announced that its Board of Directors approved a discretionary
     stock repurchase program whereby the Company may spend up to $10 million
     dollars for the repurchase of shares of its Common Stock, in the open
     market or in private transactions, from time to time, subject to prevailing
     market conditions. The Company had 10,415,012 shares of Common Stock issued
     and outstanding as of September 30, 1998, net of treasury shares.

     An unsecured bank line of credit of $10.0 million is subject to annual
     renewal. Amounts outstanding under this line are payable upon demand by the
     bank. During the first nine months of 1998, the Company incurred no
     borrowings under the line and had no balances outstanding as of September
     30, 1998. During the first nine months of 1997, the Company borrowed
     various amounts up to $2.5 million of which no balance remained outstanding
     as of September 30, 1997.

     The Company did not incur any other short-term borrowings during the first
     nine months of 1998 and 1997.

     YEAR 2000 Issue

     The "Year 2000 Issue" (Y2K) relates to problems that may result from the
     incorrect processing of information using dates or date sensitive data by
     computers and other machines utilizing embedded microprocessors. The
     problem is attributable to the computer or software recognizing the year as
     a two digit number "00" as opposed to the Year "2000". As Year 2000
     approaches, uncertainty relating to these Y2K issues must be addressed in
     order to correct the problem or properly plan contingencies to handle
     anticipated issues, if any.

     The Company started addressing the Y2K issue in 1996 and has been following
     a plan, in phases, to identify, inventory, prioritize and correct all known
     Y2K issues. The project plan incorporates the various phases and will
     evaluate both information technology (IT) related hardware and software as
     well as non-IT issues such as facilities operations and product related
     technology. The project will also attempt to obtain assurance from mission
     critical vendors (banks, transfer agents, manufacturing suppliers,
     utilities and other suppliers of critical services to the Company.) about
     their Y2K readiness and develop contingency plans for issues that may arise
     from the failure of those vendors to achieve Y2K compliance. The Company
     has substantially completed its review of all IT related systems and
     believes it will be Y2K compliant by mid 1999. The Company is currently in
     the identification and inventory phase of the review of non-IT systems and
     mission critical third party relationships which is expected to be
     completed by the end of the first quarter of 1999. Based on the review of
     responses from third-party vendors, the Company will prioritize the
     corrective actions required, if any, and commence the correction phase of
     the project by the end of the second quarter of 1999. The Company expects
     to begin contingency planning in the fourth quarter of 1998 and to complete
     such plans by the end of the second quarter of 1999.



                                     Page 7

<PAGE>   10


         Management's Discussion and Analysis of Financial Condition and
                          Results of Operations (Con't)


YEAR 2000 Issue (con't)

The costs to address the Y2K Issue has not been and is not expected to be
material to the Company's financial position or have a material impact on
operating results, however, there can be no assurance that the failure to 
ensure Year 2000 capability by a supplier or another third party would not have 
a material adverse effect on the Company. Since 1996 the Company has incurred 
expenses of approximately $100,000 to address the Y2K issue and anticipates 
incurring an additional $100,000 related to the Y2K issue. Anticipated 
additional costs do not consider costs, if any, related to the failure of third 
party relationships to become "Year 2000" compliant. All expenses incurred to 
date have been recognized as expense in the Company's consolidated financial 
statements in the period incurred. Costs, if any, related to the correction of 
Y2K issues caused by a third party's failure to be Y2K compliant would be 
expensed as incurred.

Based on the Y2K assessment information obtained and corrections implemented to
date, the Company believes that the Year 2000 Issue will not have a material
adverse effect on its financial position or results of operations. The Company
is currently inventorying results of a vendor compliance survey which will
facilitate the risk assessment and contingency planning phase of non-IT related
issues which will include planning for worst case scenarios.



                                     Page 8

<PAGE>   11


                              THE FIRST YEARS INC.

                           PART II - OTHER INFORMATION

Items 1 through 5 - Not Applicable

Item 6: Exhibits and Reports on Form 8-K

        (a)   Exhibits - The following exhibits are filed as part of
              this Report:

              Exhibit        Description
              -------        -----------

                27        Financial Data Schedule

        (b)   No reports on Form 8-K have been filed during the past quarter
              covered by this report.

Item 7A: Quantitative and Qualitative Disclosure about Market Risk

     At September 30, 1998, the Company held foreign currency forward contracts
     with a bank whereby the Company is committed to deliver foreign currency at
     predetermined rates. The contracts expire within one year. The Company's
     future commitment under these contracts totaled approximately $740,000 and
     the fair market value of the contracts approximated their notional amount.


                                     Page 9

<PAGE>   12

                              THE FIRST YEARS INC.


                                   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.


                                              THE FIRST YEARS INC.      
                                              --------------------      
                                                    Registrant          
                                                                        
                                                                        
                                                                        
Date   11/13/98                               /s/ John R. Beals       
    ------------------                     ----------------------------
                                           John R. Beals, Senior Vice   
                                           President and Treasurer,     
                                           Duly Authorized Officer and  
                                           Principal Financial Officer  
                                                                        





                                     Page 10

<PAGE>   13


                              THE FIRST YEARS INC.


                                  EXHIBIT INDEX



   Exhibit   Description                            Page
   -------   -----------                            ----

     27      Financial Data Schedule                 12







                                     Page 11