<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, 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 April 30, 1998
was 5,149,124.






<PAGE>   2


                              THE FIRST YEARS INC.



                                      INDEX
                                      -----
<TABLE>
<CAPTION>

                                                           Page
                                                           ----
<S>                                                        <C>
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 - 8

PART II - OTHER INFORMATION

Other information                                            9

SIGNATURES                                                   9

EXHIBIT INDEX                                               10

</TABLE>





<PAGE>   3

                              THE FIRST YEARS INC.
                      CONDENSED CONSOLIDATED BALANCE SHEETS

                                     ASSETS

<TABLE>
<CAPTION>

                                                MARCH 31,      DECEMBER 31,
                                                  1998           1997
                                               ----------     ----------- 
                                               (UNAUDITED)
 
<S>                                            <C>           <C>
CURRENT ASSETS:
 Cash and cash equivalents                     $11,785,865    $ 7,697,040
 Accounts receivable, net                       21,063,549     19,962,226
 Inventories                                    25,313,000     24,372,881
 Prepaid expenses and other assets                 344,438        414,764
 Deferred tax assets                             1,279,000      1,279,000
                                               -----------    -----------
       Total current assets                     59,785,852     53,725,911
                                               -----------    -----------

PROPERTY, PLANT, AND EQUIPMENT:
 Land                                              167,266        167,266
 Building                                        4,024,237      4,022,095
 Machinery and molds                             7,353,224      7,151,019
 Furniture and equipment                         4,046,742      3,947,144
                                               -----------    -----------
       Total                                    15,591,469     15,287,524
 Less accumulated depreciation                   8,886,196      8,441,874
                                               -----------    -----------
   Property, plant, and equipment - net          6,705,273      6,845,650
                                               -----------    -----------

TOTAL ASSETS                                   $66,491,125    $60,571,561
                                               ===========    ===========


                      LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES:
 Accounts payable                              $12,336,586    $10,004,244
 Accrued royalty expense                         2,269,240      2,051,721
 Accrued payroll expenses                          812,961      1,143,063
 Accrued selling expenses                        2,060,184      2,387,029
 Federal and state income taxes payable            891,200        159,600
                                               -----------    -----------
       Total current liabilities                18,370,171     15,745,657
                                               -----------    -----------


DEFERRED TAX LIABILITY                             816,900        816,900
                                               -----------    -----------


STOCKHOLDERS' EQUITY:
 Common stock                                      515,233        508,800
 Paid-in capital                                 7,479,597      6,534,308
 Retained earnings                              39,391,037     37,047,709
 Less: 3,409 shares of
   treasury stock (at cost)                        (81,813)       (81,813)
                                               -----------    -----------
       Total stockholders' equity               47,304,054     44,009,004
                                               -----------    -----------

TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY     $66,491,125    $60,571,561
                                               ===========    =========== 

</TABLE>

     See accompanying notes to condensed consolidated financial statements.


                                     Page 1


<PAGE>   4


                              THE FIRST YEARS INC.

               CONDENSED CONSOLIDATED STATEMENTS OF INCOME FOR THE
                   THREE MONTHS ENDED MARCH 31, 1998 AND 1997
                                   (UNAUDITED)


<TABLE>
<CAPTION>


                                            1998           1997
                                            ----           ----
<S>                                     <C>            <C>


NET SALES                               $35,686,605    $27,822,044

COST OF PRODUCTS SOLD                    21,437,630     16,644,939
                                        -----------    -----------

GROSS PROFIT                             14,248,975     11,177,105

SELLING, GENERAL, AND ADMINISTRATIVE
     EXPENSES                            10,388,107      8,404,199
                                        -----------    -----------

OPERATING INCOME                          3,860,868      2,772,906

OTHER INCOME (EXPENSE):
  Interest Expense                             (850)       (10,306)
  Interest Income                            78,310         14,902
                                        -----------    -----------

INCOME BEFORE INCOME TAXES                3,938,328      2,777,502

PROVISION FOR INCOME TAXES                1,595,000      1,111,000
                                        -----------    -----------

NET INCOME                              $ 2,343,328    $ 1,666,502
                                        ===========    ===========



BASIC EARNINGS PER SHARE                      $0.46          $0.34
                                              =====          =====

DILUTED EARNINGS PER SHARE                    $0.44          $0.32
                                              =====          =====


PROFORMA EARNINGS PER SHARE (NOTE 2):


BASIC EARNINGS PER SHARE                      $0.23          $0.17
                                              =====          =====

DILUTED EARNINGS PER SHARE                    $0.22          $0.16
                                              =====          =====

</TABLE>


     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, 1998 AND 1997
                                   (UNAUDITED)

<TABLE>
<CAPTION>

                                                    1998            1997
                                                    ----            ----
<S>                                               <C>            <C>

CASH FLOWS FROM OPERATING ACTIVITIES:
 Net income                                      $ 2,343,328    $ 1,666,502
 Adjustments to reconcile net income to net
  cash provided by (used for) operating
   activities:
    Depreciation                                     444,322        366,283
    Provision for doubtful accounts                  223,834        126,261
Increase (decrease) arising from working
    capital items:
    Accounts receivable                           (1,325,157)    (4,847,613)
    Inventories                                     (940,119)    (1,691,155)
    Prepaid expenses and other assets                 70,326       (190,635)
    Accounts payable                               2,332,342       (420,412)
    Accrued royalty expense                          217,519        555,025
    Accrued payroll expenses                        (330,102)       (89,899)
    Accrued selling expenses                        (326,845)      (295,252)
    Federal and state income taxes - net             731,600        872,300
                                                 -----------    -----------

     Net cash provided by (used for)
       operating activities                        3,441,048     (3,948,595)
                                                 -----------    ------------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Expenditures for property, plant,
         and equipment                              (303,945)      (394,241)
                                                 -----------    -----------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Common stock issued under stock
     option plans                                    461,422         90,191
   Tax benefit of stock option compensation          490,300            -
   Repayment of short-term borrowings                     -       1,700,000
   Repayment of industrial revenue bonds                  -         (33,333)
                                                 -----------    -----------

     Net cash provided by
       financing activities                          951,722      1,756,858
                                                 -----------    -----------

INCREASE (DECREASE) IN CASH
  AND CASH EQUIVALENTS                             4,088,825     (2,585,978)

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

CASH AND CASH EQUIVALENTS, END OF PERIOD         $11,785,865   $  1,578,609
                                                 ===========   ============  


SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:

      Cash paid for:
         Interest                                       $850        $10,306
                                                        ====        =======
         Income Taxes                               $373,100       $212,370
                                                    ========       ========
</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 consolidated balance sheet as of that
     date. All other condensed consolidated 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 March
     31, 1998, and the results of operations and cash flows for the periods
     ended March 31, 1998 and 1997.

2.   The company has 15,000,000 authorized shares of $.10 par value common stock
     with 5,148,924 and 5,084,591 shares issued and outstanding as of March 31,
     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 a 100% stock dividend payable to stockholders of
     record on May 29, 1998. Distribution of new shares are payable on June 29,
     1998.

     Additionally, on May 8, 1998 the Board of Directors authorized a $0.12 per
     share ($0.06 post-split basis) annual cash dividend payable 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: (All share and per share numbers are presented on a
     pre-split basis)
<TABLE>
<CAPTION>



                                                          Income            Shares        Per Share
                                                        (Numerator)      (Denominator)      Amount
                                                        -----------      -------------     --------
<S>                                                     <C>              <C>               <C>

      For the Quarter Ended March 31, 1997:

      Net income....................................    $1,666,502
                                                        ----------
      Basic EPS
      Income available to common
        Stockholders................................     1,666,502        4,950,701          $0.34
                                                                                             =====
      Effect of Dilutive Securities
      Incentive stock options.......................                        185,310
                                                        ----------        ---------
      Diluted EPS
      Income available to common stockholders
        and assumed conversions......................   $1,666,502        5,136,011          $0.32
                                                        ===========       =========          =====

</TABLE>



                                     Page 4


<PAGE>   7


                              THE FIRST YEARS INC.

              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS

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

<TABLE>
<CAPTION>


                                                                Income              Shares          Per Share
                                                              (Numerator)        (Denominator)        Amount
                                                              -----------        -------------        ------
<S>                                                            <C>                 <C>                <C>

      For the Quarter Ended March 31, 1998:

      Net income.........................................      $2,343,328
                                                               ----------
      Basic EPS
      Income available to common
        stockholders....................................        2,343,328           5,096,320           $0.46
                                                                                                        =====

      Effect of Dilutive Securities
      Incentive stock options...........................                              197,949
                                                               -----------          ---------

      Diluted EPS
      Income available to common stockholders
        and assumed conversions.........................        $2,343,328          5,294,269           $0.44
                                                                ==========          =========           =====

</TABLE>


     As of March 31, 1997, options to purchase 15,000 and 6,000 shares of common
     stock at $17 3/4 and $17 1/8 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 2007 and 2006, respectively, were still outstanding at March 31,
     1998.

     As of March 31, 1998, options to purchase 354 and 28,145 shares of common
     stock at $30 1/8 and $31 1/8 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 March 31, 1998.

4.   The results of operations for the three month period ended March 31, 1998 
     and 1997 are not necessarily indicative of the results to be expected for 
     the full year.

5.   During the first three 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 $2,200,000 of which
     $1,700,000 remained outstanding as of March 31, 1997 at a weighted average
     interest rate of 7.94%.

     During the first three months of 1997, the Company had available an
     unsecured line of credit from a second bank totaling $10,000,000. No
     borrowings were incurred during the period and no balances were outstanding
     as of March 31, 1997. During 1997, the line was subject to annual renewal
     and was not renewed at the option of the Company.

                                     Page 5


<PAGE>   8


                              THE FIRST YEARS INC.

              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS

     No other short-term borrowings were incurred by the Company during the
     first three months of 1998 or 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. The Company has not
     determined the effects, if any, that these standards will have on its
     consolidated financial statements.










                                     Page 6


<PAGE>   9


                              THE FIRST YEARS INC.

         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 such
Annual Report on Form 10-K for the year ended December 31, 1997, filed with the
Securities And Exchange Commission.

Net sales for the first three months of 1998 were $35.7 million, an increase of
$7.9 million or 28.3%, as compared to $27.8 million for the comparable period
last year. The increase was due to new product introductions and expanded retail
distribution in domestic and foreign markets.

Cost of products sold for the first three months of 1998 was $21.4 million, an
increase of $4.8 million or 28.8%, as compared to $16.6 million for the
comparable period last year. As a percentage of sales, cost of products sold in
the first three months of 1998 and 1997 remained consistent at 60.1% and 59.8%,
respectively.

Selling, general, and administrative expenses for the first three months of 1998
were $10.4 million, an increase of $2.0 million or 23.6%, as compared to $8.4
million over such expenses for the first three months of 1997. The increase
resulted primarily from costs related to increased sales volume; payroll and
payroll related costs, product development and integrated marketing
communication program expenses. As a percentage of net sales, selling, general,
and administrative expenses for the first three months of 1998 decreased to
29.1% from 30.2% in the comparable period of 1997. The decrease reflects the
economies of scale provided by the higher volume of business.

The Company continues to review the Year 2000 Issue (Y2K). Review of the
Company's internal computer systems for Y2K issues is progressing. the company
presently believes Y2K will not pose significant operational issues and is not
anticipated to be material to its financial position or results of operations in
any given year. Communications with significant suppliers, customers and service
vendors has been initiated to determine the extent of the Company's exposure
from such third party's failure to remedy their own Y2K issues. No guarantee can
be made that systems of other companies on which the Company relies upon will be
converted in time or that a failure to convert would not have a material effect
on the company.


                                     Page 7



<PAGE>   10


                              THE FIRST YEARS INC.

         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 40.5% for the
first three months of 1998 from 40.0% for the first three months of 1997.

Net working capital increased by $3.4 million in the first three months
primarily due to profitable operations. Accounts receivable increased by 
$4.7 million primarily as a result of increased sales and inventories increased
by $1.0 to meet continued demand for the company's products. Cash increased by 
$4.1 million primarily resulting from funds generated from 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 1998, the company incurred no borrowings under the    
line and no balances were outstanding as of March 31, 1998. During the first
three months of 1997, the Company borrowed various amounts up to $2.2 million
of which $1.7 million remained outstanding as of March 31, 1997.

During the first three months of 1997, the Company had available an unsecured
line of credit from a second bank totaling $10.0 million. No borrowings were
incurred during the period and no balances were outstanding as of March 31,
1997. During 1997, the line was subject to annual renewal and was not renewed at
the option of the Company.

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

Recent Accounting Pronouncements

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. The Company has not determined the effects, if any,
that these standards will have on its consolidated financial statements.


                                     Page 8
                                     

<PAGE>   11



                           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:
<TABLE>
<CAPTION>

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

         <S>      <C>

          27     Financial Data Schedule - 3/31/98
          27.1   Financial Data Schedule - 3/31/97 - Restated
          27.2   Financial Data Schedule - 6/30/97 - Restated
          27.3   Financial Data Schedule - 9/30/97 - Restated

</TABLE>

     (b)   On May 12, 1998 the Company filed a Report on Form 8-K to report the
           two-for-one stock split effected in the form of a 100% stock dividend
           on the Company's Common Stock, $.10 par value which was declared by
           the Board of Directors on May 8, 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.


                                         THE FIRST YEARS INC.
                                 ---------------------------------------
                                             Registrant



Date      5/13/98                /s/ John R. Beals
    -------------------          ---------------------------------------
                                 John R. Beals, Senior Vice
                                 President and Treasurer,
                                 Duly Authorized Officer
                                 and Principal Financial Officer



                                     Page 9


<PAGE>   12


                           EXHIBIT INDEX

<TABLE>
<CAPTION>


Exhibit           Description                               Page
-------           -----------                               ----
<S>       <C>                                               <C>

 27      Financial Data Schedule - 3/31/98                   11

 27.1    Financial Data Schedule - 3/31/97  -  Restated      12

 27.2    Financial Data Schedule - 6/30/97  -  Restated      13

 27.3    Financial Data Schedule - 9/30/97  -  Restated      14


</TABLE>

                                    Page 10