<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                   FORM 10 - Q

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

For the quarterly period ended March 31, 1998
                                      OR
[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
EXCHANGE ACT OF 1934

For the transition period from ____________________ to _______________________
           ___________________________________________________________

Commission file number   1 - 5542

                               DEXTER CORPORATION
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

CONNECTICUT                                                06 - 0321410
--------------------------------------------------------------------------------
(State or other jurisdiction of                           (I.R.S. Employer
incorporation or organization)                           Identification No.)

ONE ELM STREET, WINDSOR LOCKS, CONNECTICUT                    06096
--------------------------------------------------------------------------------
(Address of principal executive offices)                    (Zip Code)

(860) 292-7675
--------------
(Registrant's telephone number, including area code)

The Dexter Corporation
--------------------------------------------------------------------------------
(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 / /

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

<TABLE>
<CAPTION>
       CLASS                                Outstanding at April 30, 1998
       -----                                -----------------------------
<S>                                         <C>
COMMON STOCK, PAR VALUE $1                        23,227,567 SHARES
</TABLE>
<PAGE>   2
                                    PART I

                              FINANCIAL INFORMATION

Item 1 -     Financial Statements

         Reference is made to the following consolidated financial statements
         which are incorporated herein by reference:

         (a)      Exhibit 99a - Condensed Statement of Income for the three
                  months ended March 31, 1998 and 1997.

         (b)      Exhibit 99b - Condensed Statement of Financial Position as of
                  March 31, 1998, December 31, 1997, and March 31, 1997.

         (c)      Exhibit 99c - Condensed Statement of Cash Flows for the three
                  months ended March 31, 1998 and 1997.

         (d)      Exhibit 99d - Statement of Comprehensive Income (Loss) for the
                  three months ended March 31, 1998 and 1997.

         (e)      Exhibit 99e - Net Sales by Market for the three months ended
                  March 31, 1998 and 1997.

         (f)      Exhibit 99f - Notes to Consolidated Financial Statements.

         The unaudited financial data included herein as of March 31, 1998 and
         1997, and for the three-month periods then ended, have been reviewed by
         the registrant's independent public accountants, Coopers & Lybrand
         L.L.P., and their report is attached.


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

Analysis of Operations

The Company reported record first quarter 1998 net income of $14.2 million, or
$.61 per share on a diluted basis, compared with $12.9 million, or $.54 per
share diluted for the first quarter of 1997. Net income increased 11% while both
basic earnings per share and diluted earnings per share improved 13% in the
first quarter.

Sales in 1998 were a first quarter record at $289.9 million, an increase of 6%
compared with sales of $272.3 million in the first quarter of 1997. A 7%
increase in unit volume and a 3% increase due to acquisitions were partially
offset by a 3% unfavorable effect of currency translation rates and price
decreases averaging 1%.
<PAGE>   3
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

Products with strong performance in the first quarter include aerospace
adhesives and coatings, liquid encapsulant materials serving the electronics
market, magnetic materials, food and specialty can coatings serving
international markets, and sales of products at Life Technologies, Inc. Products
with weaker performance in the quarter include beer and beverage can coatings
serving international markets, nonwoven materials serving the food packaging
market, and printed wiring board products serving the electronics market.

Consolidated gross margin of 36.3% for the first quarter of 1998, stated as a
percentage of sales, increased .7 percentage points from 35.6% in the first
quarter of 1997. This improvement came from wholly owned Dexter operations,
primarily due to volume increases, productivity improvements, and favorable
product mix.

Marketing and administrative cost increased $5 million, or 9%, in the first
quarter of 1998 primarily due to increased cost at Life Technologies, Inc. and
marketing and administrative costs associated with businesses acquired
subsequent to the first quarter of 1997.

Other income of $2.3 million in the first quarter of 1998 decreased $1.9 million
from the first quarter of 1997. This decrease was primarily due to lower equity
income resulting from the divestiture of D & S Plastics International, which was
effective April 1, 1997. The negative impact of lower equity income was offset
by lower interest expense, a lower effective tax rate of 35% in the first
quarter of 1998 compared with 36% in 1997, and lower minority interest expense
in 1998.

Analysis of Financial Condition

Excess acquisition cost as of March 31, 1998 was $97.8 million, an increase of
$17.4 million, compared with $80.4 million as of March 31, 1997. This was
primarily due to an increase of $24.1 million due to the impact of businesses
acquired subsequent to the first quarter of 1997 which was partially offset by
$6.1 million of amortized costs.

Other assets as of March 31, 1998 were $74 million, a decrease of $15.5 million
compared with $89.5 million as of March 31, 1997. This decrease was primarily
due to the divestiture of the Company's 50% equity interest in D & S Plastics
International of $43.2 million, which was effective April 1, 1997. Partially
offsetting this decrease was an increase of 28.6 million for patents,
technology, formulas and covenants related to businesses acquired subsequent to
the first quarter of 1997.
<PAGE>   4
                                     PART II

                                OTHER INFORMATION


Item 4  - Submission of Matters to a Vote of Security Holders

         The annual meeting of the shareholders of the Company was held on April
         23, 1998, where the following actions were taken:

    (a)  The re-election to the Board of Directors of Mr. Robert M. Furek,
         chairman of the State Board of Trustees for the Hartford, Connecticut
         public school system and a partner in Resolute Partners; Mrs. Martha
         Clark Goss, vice president and chief financial officer of Booz, Allen &
         Hamilton Inc.; and Mr. Edgar G. Hotard, president and chief operating
         officer of Praxair, Inc.

         The votes for each director were as follows:

<TABLE>
<CAPTION>
         Director                   For          Against
         --------                   ---          -------
<S>                             <C>              <C>
         Robert M. Furek        20,640,815       173,612
         Martha Clark Goss      20,653,315       161,112
         Edgar G. Hotard        20,637,056       177,371
</TABLE>

         In addition, the following directors continue in office for the
         terms expiring as indicated:  Ms. Henrietta Holsman Fore (1999), Mr.
         Bernard M. Fox (1999), Mr. K. Grahame Walker (1999), George M.
         Whitesides, Ph.D. (1999), Mr. Charles H. Curl (2000), Mr. Peter G.
         Kelly (2000), and Mr. Jean-Francois Saglio (2000).

    (b)  The selection of Coopers & Lybrand L.L.P. as auditors of the Company
         for the year 1998 was ratified.

         The votes for selection of Coopers & Lybrand L.L.P. were as follows:

<TABLE>
<CAPTION>
         For                  Against        Abstain
         ---                  -------        -------
<S>                           <C>           <C>
         20,780,101            8,497         25,829
</TABLE>

    (c)  An amendment to the Company's Restated Certificate of Incorporation to
         change the Company's name to "Dexter Corporation" was approved.

         The votes for the approval of the amendment were as follows:

<TABLE>
<CAPTION>
         For                  Against        Abstain
<S>                           <C>           <C>
         20,534,844           239,067        57,515
</TABLE>
<PAGE>   5
Item 5  - Other Information

    (a)  Glen L. Urban, Ph.D., whose term as director expired on April 23, 1998,
         did not stand for re-election. Dr. Urban had served on the Board of
         Directors since 1989.

    (b)  The Board of Directors elected Mr. Jeffrey W. McClelland and Mr. David
         Woodhead to serve as vice presidents of the Company. In addition, Mr.
         McClelland is president of Adhesive & Coating Systems and Mr. Woodhead
         is president of Magnetic Technologies.

Item 6  - Exhibits and Reports on Form 8 - K

    (a)  Exhibit 3A(1) - Amendment to the Restated Certificate of Incorporation
         of the registrant, filed with the Secretary of the State of Connecticut
         on April 23, 1998, for the purposes of changing the Company's name to
         Dexter Corporation.

         Exhibit 15 of Part 1 - Letter to Securities and Exchange Commission
         re: Incorporation of Accountants' Report

         Exhibit 27 of Part 1 - Financial Data Schedule for the period ending
                                March 31, 1998. Restated Financial Data
                                Schedules for the periods ended from December
                                31, 1995 through September 30, 1997 to include
                                earnings per share - diluted due to the adoption
                                of SFAS No. 128, Earnings Per Share.

         Exhibit 99 of Part 1 - First Quarter 1998 Financial Statements and
         Notes

    (b)  No reports on Form 8 - K were filed during the quarter for which this
         report was filed.
<PAGE>   6
                                   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.



                                        DEXTER CORPORATION
                                        (Registrant)


Date  May 8, 1998

                                        /s/ Kathleen Burdett
                                        -------------------------------
                                        Kathleen Burdett
                                        Vice President and
                                        Chief Financial Officer
                                        (Principal Financial Officer)
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                                INDEX TO EXHIBITS


Exhibit No.

    3A(1)   Amendment to the Restated Certificate of Incorporation of the
            registrant, filed with the Secretary of the State of Connecticut on
            April 23, 1998.

    15      Letter to Securities and Exchange Commission re:  Incorporation of
            Accountants' Report

    27      Financial Data Schedule for the period ending March 31, 1998.
            Restated Financial Data Schedules for the periods ended December 31,
            1995 through September 30, 1997 to include earnings per share
            -diluted due to the adoption of SFAS No. 128, Earnings Per Share.

    99      First Quarter 1998 Financial Statements and Notes