<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, 1999

                                       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)

<TABLE>
<S>                                                     <C>
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)
</TABLE>

(860) 292-7675
(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  / /

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, 1999     

<S>                                      <C>
COMMON STOCK, PAR VALUE $1                   23,029,544 SHARES                
</TABLE>
<PAGE>   2
                                     PART I

                              FINANCIAL INFORMATION

Item 1 - Financial Statements

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

         (a)      Exhibit 99a - Condensed Statement of Income for the three
                  months ended March 31, 1999 and 1998.

         (b)      Exhibit 99b - Condensed Statement of Financial Position as of
                  March 31, 1999, December 31, 1998, and March 31, 1998.

         (c)      Exhibit 99c - Condensed Statement of Cash Flows for the three
                  months ended March 31, 1999 and 1998.

         (d)      Exhibit 99d - Condensed Statement of Comprehensive Income for
                  the three months ended March 31, 1999 and 1998.

         (e)      Exhibit 99e - Net Sales and Operating Income by Segment for
                  the three months ended March 31, 1999 and 1998.

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

         The unaudited financial data included herein as of March 31, 1999 and
         1998, and for the three-month periods then ended, have been reviewed by
         the registrant's independent public accountants, PricewaterhouseCoopers
         LLP, 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 first quarter 1999 net income from operations of $10.4
million, or $.45 per share on a diluted basis, compared with $14.2 million, or
$.61 per share diluted, for the first quarter of 1998. Dexter's increased
ownership of Life Technologies, Inc. created noncash amortization charges which,
together with the net impact of divestitures, reduced first quarter 1999
earnings by $.13 per share. Improved operating results in the life sciences
segment only partially offset some continuing softness in the specialty polymers
segment related to the electronics market which, although improving, is still
well below the strong first quarter of 1998.
<PAGE>   3
Item 2 - Management's Discussion and Analysis of Financial Condition and Results
         of Operations, continued

ANALYSIS OF OPERATIONS, CONTINUED

During the quarter, Dexter sold its Packaging Coatings business, including
Dexter SAS, its French industrial coatings subsidiary, and its 40% interest in
Akzo Dexter Aerospace Finishes VoF. The first quarter comparison above excludes
the gain from these divestitures of $2.53 per share. Including the gain, total
earnings for the first quarter of 1999 were $68.8 million, or $2.98 per share
diluted, compared with the $.61 per share diluted in the first quarter of 1998.

Sales in the first quarter of 1999 were $279.9 million, a decrease of 3%,
compared with sales of $289.9 million in the first quarter of 1998. Volume
increases of 4% and a 1% favorable effect of currency translation rates were
more than offset by a 6% decrease due to divestitures and price decreases
averaging 2%.

Products with strong performance in the first quarter of 1999 include products
at Life Technologies, Inc., nonwoven hygiene products, and aerospace adhesives
and specialty coatings in the specialty polymers segment. In the first quarter
of last year, the electronic materials market was still very strong.
Consequently, sales of electronic encapsulation materials, printed wiring board
products, and magnetic materials had weaker performance in the first quarter of
1999 compared with the first quarter of 1998.

Consolidated gross margin of 37.1% for the first quarter of 1999, stated as a
percentage of sales, increased .8 percentage points from 36.3% in the first
quarter of 1998. This improvement was accomplished despite charges incurred in
the first quarter of 1999 relating to Dexter's increased ownership of Life
Technologies, Inc., which unfavorably impacted gross margin by 1.2 percentage
points. Excluding these charges, gross margin improved 2.0 percentage points as
a result of increased volume and a favorable product mix at Life Technologies,
Inc.

Marketing and administrative costs increased $2.1 million, or 3%, in the first
quarter of 1999, primarily due to increased costs at Life Technologies, Inc.,
which were partially offset by lower expenses resulting from the divestiture of
the Packaging Coatings business in the first quarter of 1999.

Other income of $2.1 million in the first quarter of 1999 decreased $0.2 million
from the first quarter of 1998. The decrease was primarily due to lower equity
income resulting from the divestiture of Dexter's 40% interest in Akzo Dexter
Aerospace Finishes VoF, which was effective January 15, 1999. This decrease was
partially offset by increased interest income.

Interest expense of $6.4 million for the first quarter of 1999 increased $2.1
million, or 48%, compared with the first quarter of 1998. The increase was due
to higher average borrowings in 1999 following the acquisition of an additional
22% ownership of Life Technologies, Inc. in December 1998. These borrowings were
repaid at the beginning of March 1999 with proceeds received from the
divestiture of the Packaging Coatings business.
<PAGE>   4
Item 2 - Management's Discussion and Analysis of Financial Condition and Results
         of Operations, continued

ANALYSIS OF FINANCIAL CONDITION

Accounts receivable as of March 31, 1999 was $171.5 million, a decrease of $32.4
million and $27.9 million, respectively, compared with $203.9 million at
December 31, 1998 and $199.4 million at March 31, 1998. These decreases were
primarily due to the divestiture of the Packaging Coatings business in the first
quarter of 1999 of $44.7 million partially offset by increased receivables from
continuing operations.

Property, plant, and equipment as of March 31, 1999 was $321 million, a decrease
of $39.5 million, compared with $360.5 million at December 31, 1998. This
decrease was primarily attributable to the divestiture of the Packaging Coatings
business.

Excess of cost over net assets of businesses acquired (excess acquisition cost)
as of March 31, 1999 was $122.2 million, an increase of $24.4 million, compared
with $97.8 million as of March 31, 1998. This increase was primarily due to an
increase of $63.4 million attributable to Dexter acquiring an additional 22%
ownership of LTI in December 1998, partially offset by a decrease of $30.8
million resulting from the divestiture of the Packaging Coatings business and
amortization charges of $7.4 million. Excess acquisition cost at March 31, 1999
decreased $34.8 million from $157 million at December 31, 1998 primarily due to
the divestiture of the Packaging Coatings business and amortization charges of
$2.3 million.

Patents, technology, trademarks, and covenants as of March 31, 1999 were $115.6
million, an increase of $86.8 million, compared with $28.8 million as of March
31, 1998. This increase was primarily due to an increase of $91.5 million
attributable to Dexter's increased ownership of LTI, partially offset by
amortization charges of $3.4 million and a decrease of $1.2 million resulting
from the divestiture of the Packaging Coatings business.

Other assets were $53.5 million as of March 31, 1999, an increase of $8.3
million, compared with $45.2 million as of March 31, 1998. This increase was
primarily due to increases in deferred tax assets, partially offset by a
decrease in investments in affiliates due to the divestiture of the Company's
40% interest in Akzo Dexter Aerospace Finishes VoF in the first quarter of 1999.

Accounts payable of $77.2 million as of March 31, 1999, decreased $14.5 million
and $23.3 million, respectively, compared with $91.7 million at December 31,
1998 and $100.5 million at March 31, 1998. These decreases were primarily due to
the divestiture of the Packaging Coatings business.

Accrued liabilities and taxes as of March 31, 1999 were $130.9 million, an
increase of $37.3 million and $42 million, respectively, compared with $93.6
million as of December 31, 1998 and $88.9 million as of March 31, 1998. These
increases were principally due to an increase in accrued taxes related to the
sale of the Packaging Coatings business. Long-term deferred income taxes were
$45.4 million as of March 31, 1999, an increase of $23.2 million, compared with
$22.2 million as of March 31, 1998. This increase was also primarily due to
increased deferred taxes related to the sale of the Packaging Coatings business.
<PAGE>   5
Item 2 - Management's Discussion and Analysis of Financial Condition and Results
         of Operations, continued

ANALYSIS OF FINANCIAL CONDITION, CONTINUED

Long-term debt was $164 million as of March 31, 1999, a decrease of $218.2
million, compared with $382.2 million as of December 31, 1998. This decrease was
primarily due to the repayment of long-term borrowings, related to the increased
ownership of LTI, with proceeds received from the divestiture of the Packaging
Coatings business.

Minority interests of $85 million as of March 31, 1999 decreased $26.1 million
compared with $111.1 million as of March 31, 1998. This decrease was primarily
due to Dexter's increased ownership of LTI. As a result, Dexter's ownership in
LTI increased to approximately 71% from approximately 52% at March 31, 1998.

LIQUIDITY AND CAPITAL RESOURCES 

The Company's liquidity is strong and ample lines of credit are available to the
Company and its subsidiaries. As shown in the Condensed Statement of Cash Flows,
cash provided from operations of $3.2 million and investment activities of
$212.6 million exceeded cash needed from financing activities of $198.5 million,
thereby increasing cash for the first three months of 1999 by $17.3 million.

Investment activity for the first three months of 1999 included cash received
from divestitures of $228.7 million, primarily related to the divestiture of the
Packaging Coatings business, including Dexter SAS. Also included in investment
activity during the first quarter of 1999 were capital expenditures of $17
million.

Financing activities for the first three months of 1999 included cash outflows
principally used for the repayment of long-term debt of $216 million, which was
primarily related to the increased ownership of LTI, the purchase of 250,500
shares of the Company's outstanding common stock for $7.2 million, and dividend
payments of $6 million. Cash proceeds of $31.3 million related to new short-term
debt were included in financing activities for the first quarter of 1999.

The Company plans to meet its future working capital and capital expenditure
needs with funds provided from operations, the reduction of short-term
securities and, as needed, short-term and long-term borrowings.
<PAGE>   6
Item 2 - Management's Discussion and Analysis of Financial Condition and Results
         of Operations, continued

IMPACT OF THE YEAR 2000

General

The year 2000 issue is the result of computer programs being written using two
digits rather than four digits to define the applicable year. Any of the
Company's systems, equipment, or hardware that have date-sensitive software or
embedded chips may recognize a date using "00" as the year 1900 rather than the
year 2000. This could result in a system failure or miscalculations causing
disruption of operations, including, among other things, a temporary inability
to properly manufacture products, process transactions, send invoices, or engage
in similar normal business activities.

Based on its initial assessments, the Company determined that it would be
required to modify or replace portions of its equipment, hardware, and software
so that affected systems will properly utilize dates beyond December 31, 1999.
The Company presently believes that, with modifications and replacement of
existing equipment, hardware, and software, the year 2000 issue will be
mitigated.

Project Plan & Status

The Company's plan to resolve the year 2000 issue is being implemented by each
of the Company's businesses and involves five phases: inventory; risk
assessment, prioritization, and ownership assignment; compliance research;
remediation; and testing. The inventory phase and the risk assessment,
prioritization, and ownership assignment phase, which were performed
concurrently, are substantially complete. The compliance research phase is also
substantially complete. The remediation and testing phases are expected to
be substantially completed by September 30, 1999. Although the Company's year
2000 plan is being completed on a business by business basis, it is estimated
that the remediation phase is approximately 80% to 85% complete, and the testing
phase is approximately 40% to 50% complete.

The Company's year 2000 inventory of potentially affected items is segregated
into four categories: business applications (developed software, customized
extensions to purchased software and system interfaces), tools and platforms
(purchased commercial products, both hardware and software), intelligent devices
(manufacturing, laboratory, office, and facilities equipment), and external
business partners (suppliers, customers, and other service providers). Business
applications and tools and platforms are considered information technology
("IT") systems while intelligent devices and external business partners are
considered non-IT systems.

Concerning IT systems, two of the Company's businesses will replace most of
their existing applications with a year 2000 compliant version of new enterprise
resource planning ("ERP") software. Those legacy systems for these businesses
that will not be replaced by the ERP system will either be made year 2000
compliant or replaced. Two businesses are in the process of "repairing" (i.e.,
making year 2000 compliant) their existing core business systems and will
replace some portions of their software with year 2000 compliant software. The
remaining business has upgraded their core business applications to a year
2000 compliant software version and is in the process of testing these
applications for year 2000 compliancy.
<PAGE>   7
Item 2 - Management's Discussion and Analysis of Financial Condition and Results
         of Operations, continued

IMPACT OF THE YEAR 2000, CONTINUED

With respect to non-IT systems, the Company has dedicated resources to assist
its businesses with identifying potentially affected intelligent devices and is
using an outside firm that has a proprietary year 2000 compliance status
database to assist in the compliance research for these devices. Determination
of compliance status, remediation, and testing of these devices may be more
difficult than IT systems, as some of the manufacturers of potentially affected
equipment may no longer be in business.

The external business partners category primarily includes the process of
identifying and prioritizing critical suppliers and customers and communicating
with them about their plans and progress in addressing the year 2000 problem.
The Company has established a questionnaire to be used by the businesses for
obtaining this information from key business partners. To date, the Company is
not aware of any problems that would materially impact results of operations,
liquidity, or capital resources. However, the Company has no means of insuring
that these parties will be year 2000 ready and the inability of these parties to
successfully complete their year 2000 compliance program could impact the
Company. For key business partners, the initial assessments are evaluated and,
as deemed necessary, follow-up assessments are made. We expect this process to
be ongoing throughout 1999.

The Company is in the process of developing detailed contingency and business
continuation plans for each business to address potential year 2000 exposures.

Costs

The Company utilizes both internal and external resources to repair or replace,
test, and implement the software and operating equipment for year 2000
modifications. The total cost of the year 2000 project is estimated at between
$6 and $7 million and is being funded through operating cash flows. To date, the
Company has incurred approximately $3.9 million (approximately 50% expensed and
50% capitalized) related to all phases of the year 2000 project. The remaining
project costs are attributable to either repair or replacement of equipment,
hardware, and software and will be expensed as incurred or capitalized, as
appropriate.

Risks

The failure to remediate a material year 2000 problem could result in an
interruption in, or a failure of, certain normal business activities or
operations, including the ability to produce or deliver products to customers.
Such failures could materially or adversely affect the Company's results of
operations, liquidity, and financial condition. Due to the general uncertainty
inherent in the year 2000 problem, the Company is unable to determine with
certainty at this time whether the consequences of year 2000 failures will have
a material impact on the Company. The Company's year 2000 plan is expected to
significantly reduce the Company's level of uncertainty about the year 2000
problem. The Company believes that by executing its year 2000 plan in a timely
manner, the possibility of significant interruptions of normal operations should
be reduced.
<PAGE>   8
Item 2 - Management's Discussion and Analysis of Financial Condition and Results
         of Operations, continued

IMPACT OF THE YEAR 2000, CONTINUED

The Company plans to complete the year 2000 project are based on management's
best estimates, which were derived utilizing numerous assumptions of future
events including, but not limited to, the continued availability of certain
resources and other factors. Estimates of the status of completion and the
expected completion dates are based on tasks completed to date compared to all
required tasks. However, there can be no guarantee that expected completion
dates will be met, and actual results could differ materially from those
forecasted. Specific factors that might cause such material differences include,
but are not limited to, the availability and cost of personnel trained in
certain areas, the ability to locate and correct all relevant equipment, devices
and computer codes, and similar uncertainties.

Item 3 - Quantitative and Qualitative Disclosures about Market Risk

In the first quarter of 1999, the Company sold its Packaging Coatings business,
including Dexter SAS, its French industrial coatings subsidiary. As a result,
the Company no longer has any foreign currency exposures relating to foreign
operations of the Packaging Coatings business. Therefore, in March 1999, the
Company redenominated its Swiss franc 29.9 million floating rate long-term
borrowing due in 2003 into a Euro 18.7 million floating rate long-term borrowing
with terms and conditions which exactly mirror the original Swiss franc debt.
The redenomination was effected to hedge certain of the Company's remaining net
asset investments in foreign operations. The Company also terminated the
interest rate exchange agreement applicable to the Swiss franc debt and entered
into a new interest rate swap agreement expiring in 2003 to limit exposures to
interest rate volatility on the Euro 18.7 million floating rate promissory note.
The swap resulted in a fixed annual rate of 3.975%.

The Company's currency exposures vary, but as of March 31, 1999, are primarily
concentrated in the Euro, British Pound Sterling, Swedish Krona, and Japanese
Yen.

FORWARD LOOKING STATEMENTS

Statements made in this report that are not historical are forward-looking
statements, and as such, are subject to a number of risks. These risks,
including those pertaining to the year 2000 issue, and other risks and
uncertainties, are detailed in Dexter's Form 10-K, for the year ended December
31, 1998.
<PAGE>   9
                                     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
         22, 1999, where the following actions were taken:

   (a)   The re-election to the Board of Directors of Mrs. Henrietta Holsman
         Fore, Chairman and Chief Executive Officer of Holsman International
         and Chairman and President of Stockton Products; Mr. Bernard M. Fox,
         Consultant, Corporate and Energy Strategy; Mr. K. Grahame Walker,
         Chairman and Chief Executive Officer of Dexter Corporation; and Mr.
         George M. Whitesides, Ph.D., Professor of Chemistry at Harvard
         University.

         The votes for each director were as follows:

<TABLE>
<CAPTION>
         Director                           For             Against
         --------                           ---             -------
<S>                                      <C>                <C>   
         Henrietta Holsman Fore          20,135,429         70,839
         Bernard M. Fox                  20,102,150         104,118
         K. Grahame Walker               20,111,607         94,661
         George M. Whitesides            20,125,878         80,390
</TABLE>

         In addition, the following directors continue in office for the
         terms expiring as indicated:  Mr. Charles H. Curl (2000), Mr. Peter
         G. Kelly (2000), Mr. Jean-Francois Saglio (2000), Mr. Robert M.
         Furek (2001), Mrs. Martha Clark Goss (2001), and Mr. Edgar G. Hotard
         (2001).

   (b)   The selection of PricewaterhouseCoopers LLP as auditors of the Company
         for the year 1999 was ratified.

         The votes for selection of PricewaterhouseCoopers LLP were as follows:

<TABLE>
<CAPTION>
         For              Against        Abstain
         ---              -------        -------
<S>                       <C>            <C>   
         20,155,068       25,300         25,900
</TABLE>

   (c)   The proposal to adopt the Company's 1999 Long-Term Incentive Plan was
         approved.

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

<TABLE>
<CAPTION>
         For              Against        Abstain
         ---              -------        -------
<S>                       <C>            <C>   
         13,436,716      3,618,832       84,940
</TABLE>
<PAGE>   10
Item 5 - Other Information

         Effective in March 1999, Mr. Dale J. Ribaudo was appointed Vice
         President and Controller of the Company.  Prior to his appointment,
         Mr. Ribaudo was Treasurer of the Company.

Item 6 - Exhibits and Reports on Form 8-K

    (a)  Exhibit 10M - Dexter Corporation's 1999 Long-Term Incentive Plan was
         filed as Exhibit 4.1 to the registrant's registration statement on Form
         S-8 (File No. 333-76873) dated April 22, 1999 and is hereby
         incorporated herein by reference.

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

         Exhibit 27 of Part 1 - Financial Data Schedule

         Exhibit 99 of Part 1 - First Quarter 1999 Financial Statements and
         Notes

    (b)  On January 12, 1999, a report on Form 8-K (File No. 1-5542) was filed
         for Item 2, Acquisition of Assets, pursuant to section 13 or 15 (d) of
         the Securities Exchange Act of 1934.

         On March 11, 1999, a report on Form 8-K/A (File No. 1-5542) was filed
         as an amendment to the report on Form 8-K filed January 12, 1999, for
         Item 7, Financial Statements and Exhibits, pursuant to section 13 or 15
         (d) of the Securities Exchange Act of 1934.

         On March 15, 1999, a report on Form 8-K (File No. 1-5542) was filed for
         Item 2, Disposition of Assets, pursuant to section 13 or 15 (d) of the
         Securities Exchange Act of 1934.
<PAGE>   11
                                  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 13, 1999                        /s/ Kathleen Burdett
      ------------------                --------------------------------------  
                                        Kathleen Burdett
                                        Vice President and
                                        Chief Financial Officer
                                        (Principal Financial Officer)





Date     May 13, 1999                        /s/ Dale J. Ribaudo
      ------------------                --------------------------------------  
                                        Dale J. Ribaudo
                                        Vice President and Controller
                                        (Principal Accounting Officer)
<PAGE>   12
                              INDEX TO EXHIBITS

Exhibit No.

   10M      Dexter Corporation's 1999 Long-Term Incentive Plan was filed as
            Exhibit 4.1 to the registrant's registration statement on Form S-8
            (File No. 333-76873) dated April 22, 1999, and is hereby
            incorporated herein by reference.

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

    27      Financial Data Schedule

    99      First Quarter 1999 Financial Statements and Notes