<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                        March 31, 2001
--------------------------------------------------------------------------------

       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)

                                       n/a
--------------------------------------------------------------------------------
              (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 April 30, 2001
was 9,177,576.

<PAGE>   2


                              THE FIRST YEARS INC.



                                      INDEX


                                                               Page
PART I - FINANCIAL INFORMATION:

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 - 6

Management's Discussion and Analysis of Financial
  Condition and Results of Operations                         7 - 9

Quantitative and Qualitative Disclosure about
  Market Risk                                                     9

PART II - OTHER INFORMATION

Other Information                                                10

SIGNATURES                                                       11

EXHIBIT INDEX                                                    12


<PAGE>   3


                    THE FIRST YEARS INC.
            Condensed Consolidated Balance Sheets

                                     ASSETS
<TABLE>
<CAPTION>

                                                March 31,      December 31,
                                                  2001            2000
                                              -------------    ------------
                                              (Unaudited)
<S>                                            <C>             <C>
CURRENT ASSETS:
  Cash and cash equivalents                    $ 18,285,244    $ 21,180,242
  Accounts receivable, net                       23,634,919      19,527,429
  Inventories                                    16,914,400      18,443,713
  Prepaid expenses and other assets               1,515,828         756,357
  Deferred tax assets                             2,069,900       2,069,900
                                               ------------    ------------
         Total current assets                    62,420,291      61,977,641
                                               ------------    ------------

PROPERTY, PLANT, AND EQUIPMENT:
  Land                                              167,266         167,266
  Building                                        5,302,561       5,254,150
  Machinery and molds                             7,668,010       7,233,145
  Furniture and equipment                         6,626,307       6,269,346
                                               ------------    ------------
         Total                                   19,764,144      18,923,907
  Less accumulated depreciation                   9,739,994       9,207,168
                                               ------------    ------------
         Property, plant, and equipment - net    10,024,150       9,716,739
                                               ------------    ------------

TOTAL ASSETS                                   $ 72,444,441    $ 71,694,380
                                               ============    ============

                 LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES:
  Accounts payable and accrued expenses        $ 12,017,185    $ 11,605,240
  Accrued royalty expenses                          772,565         946,623
  Accrued selling expenses                        1,271,125       3,023,528
                                               ------------    ------------
         Total current liabilities               14,060,875      15,575,391
                                               ------------    ------------

DEFERRED TAX LIABILITY                            1,216,200       1,216,200
                                               ------------    ------------

STOCKHOLDERS' EQUITY
  Common stock                                    1,072,574       1,067,934
  Paid-in-capital                                 9,023,440       8,714,711
  Retained earnings                              63,362,398      60,985,483
   Less treasury stock at cost, 1,547,739
   and 1,503,572 shares as of March 31,
   2001 and December 31, 2000, respectively     (16,291,046)    (15,865,339)
                                               ------------    ------------
                  Total stockholders' equity     57,167,366      54,902,789
                                               ------------    ------------

TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY     $ 72,444,441    $ 71,694,380
                                               ============    ============
</TABLE>



     See accompanying notes to condensed consolidated financial statements.

                                     Page 1


<PAGE>   4





                              THE FIRST YEARS INC.

                  Condensed Consolidated Statements of Income
                   Three Months Ended March 31, 2001 and 2000
                                  (Unaudited)



                                     2001            2000
                                 -----------     -----------
NET SALES                        $33,785,140     $36,762,253

COST OF PRODUCTS SOLD             21,261,929      23,638,046
                                 -----------     -----------
GROSS PROFIT                      12,523,211      13,124,207

SELLING, GENERAL AND
  ADMINISTRATIVE EXPENSES          8,683,648       8,255,244
                                 -----------     -----------
OPERATING INCOME                   3,839,563       4,868,963

OTHER INCOME:

  Interest Income                    189,152         150,270
                                 -----------     -----------
INCOME BEFORE INCOME TAXES         4,028,715       5,019,233

PROVISION FOR INCOME TAXES         1,651,800       2,007,700
                                 -----------     -----------
NET INCOME                       $ 2,376,915     $ 3,011,533
                                 ===========     ===========
BASIC EARNINGS PER SHARE         $      0.26     $      0.31
                                 ===========     ===========
DILUTED EARNINGS PER SHARE       $      0.26     $      0.31
                                 ===========     ===========


     See accompanying notes to condensed consolidated financial statements.

                                     Page 2


<PAGE>   5


                              THE FIRST YEARS INC.

             Condensed Consolidated Statements of Cash Flows for the
                   Three Months Ended March 31, 2001 and 2000
                                   (Unaudited)
<TABLE>
<CAPTION>

                                                                                         2001             2000
                                                                                     ------------      ------------
<S>                                                                                  <C>               <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
         Net income                                                                  $  2,376,915      $  3,011,533
         Adjustments to reconcile net income to net cash provided by operations:
         Depreciation                                                                     532,826           534,542
         Provision for doubtful accounts                                                    5,056            26,829
  Increase (decrease) arising from working capital items:
         Accounts receivable                                                           (4,112,546)       (7,414,905)
         Inventories                                                                    1,529,313         3,779,145
         Prepaid expenses and other expenses                                             (738,071)          452,028
         Accounts payable and accrued expenses                                            411,945          (149,909)
         Accrued royalties                                                               (174,058)         (876,885)
         Accrued selling expense                                                       (1,752,403)         (887,521)
         Deferred income taxes                                                                  0           (35,500)
                                                                                     ------------      ------------
             Net cash used by operating activities                                     (1,921,023)       (1,560,643)
                                                                                     ------------      ------------
CASH FLOWS FROM INVESTING ACTIVITIES:
         Expenditures for property, plant, and
          equipment                                                                      (840,237)         (608,308)
                                                                                     ------------      ------------
CASH FLOWS FROM FINANCING ACTIVITIES:
         Common stock issued under stock option
          plans                                                                           159,462           405,872
         Purchase of treasury stock .                                                    (293,200)         (290,088)
                                                                                     ------------      ------------

             Net cash used for financing activities                                      (133,738)          115,784
                                                                                     ------------      ------------

DECREASE IN CASH AND CASH EQUIVALENTS                                                  (2,894,998)       (2,053,167)
                                                                                     ------------      ------------

CASH AND CASH EQUIVALENTS, BEGINNING OF PERIOD                                         21,180,242        13,400,728
                                                                                     ------------      ------------

CASH AND CASH EQUIVALENTS, END OF PERIOD                                             $ 18,285,244      $ 11,347,561
                                                                                     ============      ============
SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:
         Cash paid for:
                  Income taxes                                                       $    170,000      $    218,000
                                                                                     ============      ============
SUPPLEMENTAL SCHEDULE OF NONCASH FINANCING ACTIVITIES:
       Treasury stock transactions                                                   $    132,507      $          0
                                                                                     ============      ============
</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, 2000 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 recurring adjustments necessary to present fairly
   the financial position as of March 31, 2001, and the results of operations
   and cash flows for the periods ended March 31, 2001 and 2000. Certain
   reclassifications were made to prior year amounts in order to conform to the
   current year presentation.

2. The Company has 50,000,000 authorized shares of $.10 par value
   common stock with 9,177,576 and 9,175,765 shares issued and
   outstanding as of March 31, 2001 and December 31, 2000, respectively.

   On May 3, 2001 the Board of Directors authorized a $0.06 per share annual
   cash dividend to be paid on June 15, 2001 to holders of record at the close
   of business on May 30, 2001.

   During the first three months of 2001, the Company purchased 30,400 shares of
   the Company's common stock on the open market. The cost of the shares
   amounted to $293,200 and are currently being held as treasury shares.

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

<TABLE>
<CAPTION>
                                                         Three Months Ended
                                                              March 31,
                                                        2001            2000
                                                     ----------     ----------

<S>                                                  <C>            <C>
WEIGHTED AVERAGE SHARES OUTSTANDING                   9,177,179      9,620,683

EFFECT OF DILUTIVE SHARES                                86,413         87,229
                                                     ----------     ----------

WEIGHTED AVERAGE DILUTED SHARES OUTSTANDING           9,263,592      9,707,912
                                                     ==========     ==========

NET INCOME                                           $2,376,915     $3,011,533
                                                     ==========     ==========

BASIC EARNINGS PER SHARE                             $     0.26     $     0.31
                                                     ==========     ==========

DILUTED EARNINGS PER SHARE                           $     0.26     $     0.31
                                                     ==========     ==========
</TABLE>


                                     Page 4
<PAGE>   7

                              THE FIRST YEARS INC.

          NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS (Con't)


     As of March 31, 2001, options to purchase 732,829 shares of common stock
     were not included in the computations of diluted EPS because the options'
     exercise price was greater than the average price of the Company's common
     stock. The options, which expire in 2003 to 2010, had exercise prices
     ranging from $9.125 to $17.00 per share.

     As of March 31, 2000, options to purchase 517,828 shares of common stock
     were not included in the computation of diluted EPS because the options'
     exercise price was greater than the average price of the Company's common
     shares. The options, which expire in 2002 to 2009 had exercise prices
     ranging from $8.875 to $17.75 per share.

4.   The results of operations for the three month period ended March 31, 2001
     are not necessarily indicative of the results to be expected for the full
     year.

5.   During the first three months of 2001 and 2000, the Company did not borrow
     against its $10,000,000 unsecured line of credit established with a bank.

6.   During 2000, the Securities and Exchange Commission (SEC) issued Staff
     Accounting Bulletin (SAB) No. 101, "Revenue Recognition", which provides
     the SEC staff's views in applying generally accepted accounting principles
     to revenue recognition. SAB No. 101 was effective for the Company on
     October 1, 2000. The adoption of SAB No. 101 was not material to the
     Company's consolidated financial statements.

7.   On January 1, 2001, the Company adopted the provisions of Statement of
     Financial Accounting Standards (SFAS) No. 133 "Accounting for Derivative
     Instruments and Hedging Activities". This statement establishes
     accounting and reporting standards for derivative instruments.
     Specifically, it requires that an entity recognize all derivatives as
     either assets or liabilities on the balance sheet at fair value. The
     accounting for changes in the fair value of a derivative (that is,
     unrealized gains or losses) will be recorded as a component of an entity's
     net income or other comprehensive income, depending upon designation (as
     defined in the statement). The adoption of SFAS No. 133 was not material
     to the Company's consolidated financial statements.

     In March 2000, the Financial Accounting Standards Board issued
     Interpretation No. 44 (FIN 44), "Accounting for Certain Transactions
     involving Stock Compensation", an interpretation of APB No. 25. FIN 44 was
     effective July 1, 2000. The adoption of FIN 44 was not material to the
     Company's consolidated financial statements.

                                     Page 5

<PAGE>   8

                              THE FIRST YEARS INC.

          NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS (Con't)


     During 2000, the Emerging Issues Task Force (EITF) issued EITF No. 00-10,
     "Accounting for Shipping and Handling Fees and Costs". EIFT No. 00-10
     addresses the statements of earnings classification of shipping and
     handling costs billed to customers and was effective for the fourth quarter
     of 2000. The adoption of EITF No. 00-10 resulted in a reclassification of
     prior year amounts to conform with the current year presentation.



8.   The Company derives sales from products carrying The First Years brand as
     well as products sold under licensing agreements. During the first three
     months of 2001 and 2000, products sold under The First Years brand amounted
     to $22,646,000 and $24,541,000, respectively, while net sales derived from
     license and specialty products amounted to $11,139,000 and $12,221,000 in
     the first three months of 2001 and 2000, respectively. Net export sales,
     primarily to Europe, Canada, South America, and the Pacific Rim, were
     approximately $3,462,000 and $3,821,000 during the first three months of
     2001 and 2000, respectively.






                                     Page 6

<PAGE>   9



                              The First Years Inc.

Part I, Item 2.

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

Statements in this Quarterly 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. Forward-looking statements are
typically identified by the words: believe, expect, anticipate, intend, are
confident, estimate and similar expressions which by their nature refer to
future events. Actual future results may differ materially from those
anticipated depending on a variety of factors which include but are not limited
to, continued growth in sales of The First Years brand products, the success of
new Disney character products, continued success of market research identifying
new product opportunities, successful introduction of new products, continued
product innovation, the success of new enhancements to the Company's brand
image, growth in international sales, ability to attract and retain key
personnel and growth in sales and earnings. Information with respect to risk
factors is contained in Exhibit 99 to the Company's most recent Annual Report on
Form 10-K, and its quarterly reports on Form 10-Q as filed with the Securities
and Exchange Commission. Readers are cautioned not to place undue reliance on
these forward-looking statements, which speak only as of the date hereof.

Net sales for the first three months of 2001 were $33.8 million, down from sales
of $36.8 million for the comparable period last year. The decrease was primarily
due to a decline in the sale of licensed, specialty, and The First Years brand
products over the corresponding three month period of 2000. This decline is
primarily attributable to general retail cautiousness, timing of product
shipments, and inventory cutbacks by several major customer accounts.

Cost of products sold for the first three months of 2001 was $21.3 million, a
decrease of $2.3 million (or 10%), as compared to $23.6 million for the
comparable period last year. As a percentage of sales, cost of products sold for
the first three months of 2001 decreased to 63% from 64% in the comparable
period of 2000 due to changes in product mix and cost reductions.

Selling, general, and administrative expenses for the first three months of 2001
were $8.7 million, an increase of $0.4 million or 5%, as compared to $8.3
million of related expenses for the first three months of 2000. The increase is
due primarily to higher payroll and payroll-related costs. As a percentage of
net sales, selling, general, and administrative expenses for the first three
months of 2001 increased to 26% from 22% in the comparable period of 2000.

                                     Page 7


<PAGE>   10
                              The First Years Inc.

Part I, Item 2.

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

Income tax expense as a percentage of pretax income increased to 41.0% in the
first three months of 2001 as compared to 40.0% for the first three months of
2000. The increase is due to additional state tax accruals.

Net working capital increased by $2.0 million in the first three months of 2001
to $48.4 million at March 31, 2001 from $46.4 million at December 31, 2000
primarily due to profitable operations. Accounts receivable increased by $4.1
million due to normal business fluctuations during the first three months of
2001. Cash decreased by $2.9 million to $18.3 million at March 31, 2001
primarily due to the increase in accounts receivable, which was partially offset
by profitable operations.

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 three months of 2001 and 2000, the Company incurred no borrowings
under the line and had no balances outstanding as of March 31, 2001 and 2000,
respectively. The Company did not incur any other short-term borrowings during
the first three months of 2001 and 2000.

RECENT ACCOUNTING PRONOUNCEMENTS

During 2000, the Securities and Exchange Commission (SEC) issued Staff
Accounting Bulletin (SAB) No. 101, "Revenue Recognition", which provides the SEC
staff's views in applying generally accepted accounting principles to revenue
recognition. SAB No. 101 was effective for the Company on October 1, 2000. The
adoption of SAB No. 101 was not material to the Company's consolidated financial
statements.

On January 1, 2001, the Company adopted the provisions of Statement of Financial
Accounting Standards (SFAS) No. 133, "Accounting for Derivative Instruments and
Hedging Activities". This statement establishes accounting and reporting
standards for derivative instruments. Specifically, it requires that an entity
recognize all derivatives as either assets or liabilities on the balance


                                     Page 8

<PAGE>   11

                              The First Years Inc.


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

sheet at fair value. The accounting for changes in the fair value of a
derivative (that is, unrealized gains or losses) will be recorded as a component
of an entity's net income or other comprehensive income, depending upon
designation (as defined in the statement). The adoption of SFAS No. 133 was not
material to the Company's consolidated financial statements.

In March 2000, the Financial Accounting Standards Board issued Interpretation
No. 44 (FIN 44), "Accounting for Certain Transactions involving Stock
Compensation", an interpretation of APB No. 25. FIN 44 was effective July 1,
2000. The adoption of FIN 44 was not material to the Company's consolidated
financial statements.

During 2000, the Emerging Issues Task Force (EITF) issued EITF No. 00-10,
"Accounting for Shipping and Handling Fees and Costs". EIFT No. 00-10 addresses
the statements of earnings classification of shipping and handling costs billed
to customers and was effective for the fourth quarter of 2000. The adoption of
EITF No. 00-10 resulted in a reclassification of prior year amounts to conform
with the current year presentation.

Part I, Item 3.

Quantitative and Qualitative Disclosure about Market Risk

     At March 31, 2001, 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 $2,455,000
     and the fair market value of the contracts approximated their predetermined
     rates included therein.

     Also see the Company's disclosure regarding Market Risk in Item 7A of its
     Annual Report on Form 10K for the fiscal year ended December 31, 2000, as
     filed with the SEC.

                                     Page 9


<PAGE>   12

                              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

               3(i)     Restated Articles of Organization of the Registrant
                        (filed as Exhibit (3.1) to Amendment No. 1 to the
                        Registrant's Form S-1 Registration Statement filed with
                        the Commission on October 5, 1995 [Reg. No. 33- 62673]
                        and incorporated herein by reference).

               3(ii)    By-laws of the Registrant (filed as Exhibit 3(ii) to the
                        Registrant's Annual Report on Form 10-K for the fiscal
                        year ended December 31, 1999 [File No. 0-7024] and
                        incorporated herein by reference).

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



                                     Page 10


<PAGE>   13

                              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  5/14/01                         By: /s/ John R. Beals
    ------------                         ---------------------------------------
                                          John R. Beals, Senior Vice
                                          President and Treasurer,
                                          (Duly Authorized Officer and
                                          Principal Financial Officer)



                                     Page 11


<PAGE>   14

                              THE FIRST YEARS INC.

                                  EXHIBIT INDEX


<TABLE>
<CAPTION>
   Exhibit     Description                                             Page
   -------     -----------                                             ----

<S>            <C>                                                     <C>
     3(i)      Restated Articles of Organization of the Registrant
               (filed as Exhibit (3.1) to Amendment No. 1 to the
               Registrant's Form S-1 Registration Statement filed
               with the Commission on October 5, 1995 [Reg. No.
               33-62673] and incorporated herein by reference).

      3(ii)    By-laws of the Registrant (filed as Exhibit 3(ii) to
               the Registrant's Annual Report on Form 10-K for the
               fiscal year ended December 31, 1999 [File  No. 0-7024]
               and incorporated herein by reference).
</TABLE>


                                     Page 12