<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 June 30, 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)

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)

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 June 30, 1999
<S>                                                  <C>
COMMON STOCK, PAR VALUE $1                                        23,037,976 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 and
                  six-month periods ended June 30, 1999 and 1998.

              (b) Exhibit 99b - Condensed Statement of Financial Position as of
                  June 30, 1999, December 31, 1998, and June 30, 1998.

              (c) Exhibit 99c - Condensed Statement of Cash Flows for the
                  six-month periods ended June 30, 1999 and 1998.

              (d) Exhibit 99d - Condensed Statement of Comprehensive Income for
                  the three and six-month periods ended June 30, 1999 and 1998.

              (e) Exhibit 99e - Net Sales and Operating Income by Segment for
                  the three and six-month periods ended June 30, 1999 and 1998.

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

             The unaudited financial data included herein as of June 30, 1999
             and 1998, and for the three and six-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 second quarter 1999 net income of $13.7 million, or $.60
per share on a diluted basis, compared with $16.4 million, or $.70 per share
diluted, for the second quarter of 1998. Dexter's increased ownership of Life
Technologies, Inc. created noncash amortization charges which, together with the
net impact of divestitures and acquisitions, reduced second quarter 1999
earnings by $.10 per share.

Sales in the second quarter of 1999 were $256.1 million, a decrease of 15%,
compared with sales of $302.6 million in the second quarter of 1998. Volume
increases of 5% were more than offset by an 18% decrease due to the net effect
of divestitures and acquisitions, price decreases averaging 1%, and a 1%
unfavorable effect of currency translation rates.
<PAGE>   3
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

ANALYSIS OF OPERATIONS, CONTINUED

Sales for the first six months of 1999 were $536.0 million, a 10% decrease
compared with sales of $592.5 million for the same period last year. Volume
increases of 4% were more than offset by a 13% decrease due to the net effect of
divestitures and acquisitions and price decreases averaging 1%.

Earnings from operations for the first six months of 1999 were $24.1 million, or
$1.05 per share on a diluted basis, compared with $30.6 million, or $1.31 per
share diluted, for the same period last year. Dexter's increased ownership of
Life Technologies, Inc. created noncash amortization charges which, together
with the net impact of divestitures and acquisitions, reduced earnings for the
first six months of 1999 by $.23 per share. Including the gain on divestiture of
product lines of $2.53 per share, which occurred in the first quarter of 1999,
total earnings for the first six months of 1999 were $82.6 million, or $3.58 per
share diluted, compared with the $1.31 per share diluted for the same period
last year.

Sales of nonwoven medical products and electronic encapsulation materials showed
continued improvement and were stronger in the second quarter of 1999 compared
with the second quarter of 1998. Products with strong performance in the second
quarter and first six months of 1999, compared with the same periods last year,
include products at Life Technologies, Inc., nonwoven wet wipes and specialty
coatings in the specialty polymers segment.

Sales of magnetic materials and printed wiring board products serving the
electronics market had weaker performance in both the second quarter and first
six months of 1999 compared with the same periods last year. Sales of nonwoven
food packaging products had weaker sales in the second quarter of 1999 compared
to the second quarter of 1998.

Consolidated gross margin of 39.9% for the second quarter of 1999, stated as a
percentage of sales, increased 3.3 percentage points from 36.6% in the second
quarter of 1998. Excluding charges incurred in the second quarter of 1999
relating to Dexter's increased ownership in Life Technologies, Inc., which
unfavorably impacted gross margin by 0.8 percentage points, gross margin
improved 4.1 percentage points. Gross margin of 38.4% for the first six months
of 1999 increased 1.9 percentage points compared with 36.5% for the same period
last year. Excluding the charges incurred for the first six months of 1999
relating to Dexter's increased ownership in Life Technologies, Inc., which
unfavorably impacted gross margin by 1.0 percentage point, gross margin improved
2.9 percentage points. These improvements were the result of increased volume
and a favorable product mix at Life Technologies, Inc. and the divestiture of
the lower gross margin Packaging Coatings business in the first quarter of 1999.
<PAGE>   4
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

ANALYSIS OF OPERATIONS, CONTINUED

Marketing and administrative costs increased $2.5 million, or 2%, for the first
six months of 1999 compared with the first six months of 1998. The increase was
primarily due to increased costs at Life Technologies, Inc. and higher general
corporate expenses that were partially offset by reduced expense resulting from
the Packaging Coatings divestiture in the first quarter of 1999.

Research and development expense decreased $2.1 million, or 15%, in the second
quarter of 1999 and $2.3 million, or 8%, for the first six months of 1999
compared with the same periods in 1998. These decreases were primarily due to
lower expenses resulting from the divestiture in the first quarter of 1999.

Interest expense of $11.1 million for the first six months of 1999 increased
$2.4 million, or 28%, compared with the first six months of 1998. The increase
was primarily due to higher average borrowings in the first quarter of 1999
following the acquisition of an additional 22% ownership in 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.

Minority interest expense decreased $1.7 million, or 36%, in the second quarter
of 1999 compared with the same period in 1998. This decrease was principally due
to Dexter increasing its ownership of Life Technologies, Inc. to 71% effective
in December 1998.
<PAGE>   5
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

ANALYSIS OF FINANCIAL CONDITION

Accounts receivable as of June 30, 1999 were $176.2 million, a decrease of $27.7
million and $35.9 million, respectively, compared with $203.9 million at
December 31, 1998 and $212.1 million at June 30, 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.

Prepaid and deferred expenses as of June 30, 1999 were $24.2 million, a decrease
of $4 million compared with $28.2 million at June 30, 1998. This decrease was
primarily due to the divestiture of the Packaging Coatings business.

Property, plant, and equipment as of June 30, 1999 was $331.9 million, a
decrease of $28.6 million and $24.4 million, respectively, compared with $360.5
million at December 31, 1998 and $356.3 million at June 30, 1998. These
decreases were primarily attributable to the divestiture of the Packaging
Coatings business partially offset by capital expenditures, net of depreciation.

Excess of cost over net assets of businesses acquired (excess acquisition cost)
as of June 30, 1999 was $122.8 million, an increase of $29 million, compared
with $93.8 million as of June 30, 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 $7.8 million. Excess acquisition cost at June 30, 1999
decreased $34.2 million from $157 million at December 31, 1998 primarily due to
the divestiture of the Packaging Coatings business and amortization charges of
$4.4 million.

Patents, technology, trademarks, and covenants as of June 30, 1999 were $117.3
million, an increase of $89.1 million, compared with $28.2 million as of June
30, 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 $3.9 million.

Other assets were $54.6 million as of June 30, 1999, an increase of $8.4
million, compared with $46.2 million as of June 30, 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 $69.3 million as of June 30, 1999, decreased $22.4 million
and $29.1 million, respectively, compared with $91.7 million at December 31,
1998 and $98.4 million at June 30, 1998. These decreases were primarily due to
the divestiture of the Packaging Coatings business.
<PAGE>   6
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

ANALYSIS OF FINANCIAL CONDITION, CONTINUED

Accrued liabilities and taxes as of June 30, 1999 were $116.7 million, an
increase of $21.3 million and $23.6 million, respectively, compared with $95.4
million as of December 31, 1998 and $93.1 million as of June 30, 1998. These
increases were principally due to an increase in accrued taxes related to the
gain on the sale of the Packaging Coatings business. Long-term deferred income
taxes were $45.5 million as of June 30, 1999, an increase of $23.3 million,
compared with $22.2 million as of June 30, 1998. This increase was also
primarily due to increased deferred taxes related to the gain on the sale of the
Packaging Coatings business.

Long-term debt was $199.8 million as of June 30, 1999, a decrease of $182.4
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. Long-term debt at June 30, 1999 increased by $20 million
compared with $179.8 million as of June 30, 1998. Included in this increase was
$3 million of debt related to LTI's acquisition of a process chromatography and
research products business, combined with additional borrowings used to fund
partial payment of the taxes on the gain on the sale of the Packaging Coatings
business.

Deferred items were $40.7 million as of June 30, 1999, an increase of $4.5
million compared with $36.2 million as of December 31, 1998. This increase was
primarily due to a non-compete agreement associated with the divestiture of the
Packaging Coatings business partially offset by decreased pension and
postretirement liabilities. Deferred items at June 30, 1999 increased $7.2
million from $33.5 million at June 30, 1998 primarily due to the non-compete
agreement associated with the divestiture of the Packaging Coatings business.

Minority interests of $86.7 million as of June 30, 1999 decreased $28.1 million
compared with $114.8 million as of June 30, 1998. This decrease was primarily
due to Dexter's increased ownership of LTI. Dexter's ownership in LTI increased
to approximately 71% from approximately 52% at June 30, 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 $5.7 million and investment activities of
$181.6 million were exceeded by the cash needed for financing activities of $208
million, thereby decreasing cash for the first six months of 1999 by $20.7
million.

Operating activities for the first six months of 1999 provided $5.7 million in
cash. Net income, after adjustments for the pretax gain on the divestiture of
the Packaging Coatings business, and the associated income taxes not due,
depreciation and amortization, and minority interests were the principal source
of cash from operations in 1999. Working capital increases were the principal
use of cash from operations.

Investment activity for the first six months of 1999 included cash received from
divestitures of $228.9 million, primarily related to the divestiture of the
Packaging Coatings business, including Dexter SAS. Also included in investment
activity during the first six months of 1999 were capital expenditures of $34.7
million and cash expenditures for acquisitions of $13.5 million, primarily
related to LTI's acquisition of a process chromatography and research products
business.

Financing activities for the first six months of 1999 included cash outflows
principally used for the repayment of long-term debt of $182.6 million, which
was primarily related to the increased ownership of LTI, the purchase of 344,500
shares of the Company's outstanding common stock for $10.1 million, and dividend
payments of $12 million.
<PAGE>   7
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

LIQUIDITY AND CAPITAL RESOURCES, CONTINUED

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.

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 had 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 complete. The compliance research phase is substantially
complete. The remediation and testing phases are well underway and 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 85% to 90% complete, and the testing
phase is approximately 50% to 60% 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.
<PAGE>   8
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

IMPACT OF THE YEAR 2000, CONTINUED

Concerning IT systems, two of the Company's businesses have replaced the
majority of their applications with year 2000 compliant versions of new
enterprise resource planning ("ERP") software. Remaining legacy systems for
these businesses that were not replaced by the ERP systems are being 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 have
replaced some portions of their software with year 2000 compliant software. The
remaining business has upgraded its core business applications to a year 2000
compliant version and is testing these applications to validate year 2000
compliancy.

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 includes
reliance, in some cases, on equipment manufacturer's compliance certification.

The external business partners category includes 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.
Development of these plans will be ongoing throughout 1999.

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 $4.1 million (approximately 60% expensed and
40% 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.
<PAGE>   9
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

IMPACT OF THE YEAR 2000, CONTINUED

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.

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 June 30, 1999, are primarily
concentrated in the Euro, British Pound Sterling, Swedish Krona, and Japanese
Yen.
<PAGE>   10
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

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>   11
                                     PART II

                                OTHER INFORMATION

Item 5 - Other Information

            Effective in July 1999, Mr. John B. Lockwood was appointed Vice
            President, Taxes of the Company. Prior to his appointment, Mr.
            Lockwood was Director of Taxes for the Company.

            Effective in July 1999, Ms. Rosanne S. Potter was appointed
            Treasurer of the Company. Prior to joining the Company, Ms. Potter
            served as Leader of Global Facilities Integration for Hercules,
            Incorporated, and as Treasurer of BetzDearborn, Inc. from 1996 until
            its acquisition by Hercules in 1998.

Item 6  -   Exhibits and Reports on Form 8-K

      (a)   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 - Second Quarter 1999 Financial Statements and
            Notes

      (b)   No reports on Form 8-K were filed during the quarter for which the
            report was filed.
<PAGE>   12
                                   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)

       July 30, 1999                        /s/ Kathleen Burdett
Date...........................            ...................................

                                           Kathleen Burdett
                                           Vice President and
                                           Chief Financial Officer
                                           (Principal Financial Officer)

       July 30, 1999                        /s/ Dale J. Ribaudo
Date...........................            ...................................

                                           Dale J. Ribaudo
                                           Vice President and Controller
                                           (Principal Accounting Officer)
<PAGE>   13
                                INDEX TO EXHIBITS


Exhibit No.

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

     27           Financial Data Schedule

     99           Second Quarter 1999 Financial Statements and Notes