<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 September 30, 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)

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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)
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(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.

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<S>                                              <C>
          CLASS                                  Outstanding at October 31, 1998

COMMON STOCK, PAR VALUE $1                             23,279,353 SHARES
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                                     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 and
                nine-month periods ended September 30, 1998 and 1997.

         (b)    Exhibit 99b - Condensed Statement of Financial Position as of
                September 30, 1998, December 31, 1997, and September 30, 1997.

         (c)    Exhibit 99c - Condensed Statement of Cash Flows for the
                nine-month periods ended September 30, 1998 and 1997.

         (d)    Exhibit 99d - Statement of Comprehensive Income for the three
                and nine-month periods ended September 30, 1998 and 1997.

         (e)    Exhibit 99e - Net Sales by Market for the three and nine-month
                periods ended September 30, 1998 and 1997.

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

         The unaudited financial data included herein as of September 30, 1998
         and 1997, and for the three and nine-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 third quarter 1998 net income of $14.2 million, or $.61 per
share on a diluted basis, which maintained the record level for third quarter
earnings set in 1997. An improvement in gross margin together with expense
controls supported this result.

Sales in the third quarter of 1998 were $283.4 million, a 1% decrease compared
with sales of $286.9 million in the third quarter last year. A 2% increase due
to acquisitions was offset by 1% decreases in unit volume, currency translation
effects, and average prices.
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Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

ANALYSIS OF OPERATIONS, CONTINUED

Sales for the first nine months of 1998 were $875.9 million, a 3% increase
compared with sales of $852.4 million for the same period last year. A 3%
increase in unit volume and a 2% increase due to acquisitions were partially
offset by a 1% unfavorable effect of currency translation rates and price
decreases averaging 1%.

Earnings for the first nine months of 1998 were a record $44.8 million, or $1.92
per share on a diluted basis, a 4% increase compared with $43.1 million, or
$1.84 per share diluted, for the same period last year.

Products with stronger performance in the third quarter and first nine months of
1998 compared with the same periods last year include aerospace adhesives and
coatings, food and specialty can coatings serving international markets,
nonwoven wet wipes in the medical market, and products at Life Technologies,
Inc.

Sales of electronic encapsulation materials and printed wiring board products
serving the electronics market, and beer and beverage can coatings serving
international markets had weaker performance in both the third quarter and first
nine months of 1998 compared with the same periods last year. Sales were weaker
in the third quarter 1998 compared with the third quarter of 1997 for magnetic
materials, nonwoven materials serving the international food packaging market
and the "other" segment.

Consolidated gross margin of 36.8% in the third quarter of 1998, stated as a
percentage of sales, increased .5 percentage points compared with 36.3% in the
third quarter of 1997. Gross margin of 36.6% for the first nine months of 1998
increased .6 percentage points compared with 36% for the same period last year.
These improvements came from increased volume at Life Technologies, Inc. as well
as productivity and cost containment activities.

Marketing and administrative costs increased $8.2 million, or 5%, for the first
nine months of 1998 compared with the same period in 1997, principally due to
increased costs at Life Technologies, Inc. and marketing and administrative
costs associated with businesses acquired in the fourth quarter of 1997.

Other income of $7.2 million for the first nine months of 1998 decreased $2.1
million, or 22%, compared with $9.3 million for the first nine months of 1997
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 the lower other income for the first nine months of 1998 was more than offset
by a decrease in interest expense of $2.4 million due to lower average long-term
borrowings in 1998. The effective tax rate was 35% in 1998 compared with 36% in
1997.

Minority interest expense increased $.5 million, or 13%, in the third quarter of
1998 and $1.4 million, or 13%, for the first nine months of 1998 compared with
the same periods last year, due to increased profits at Life Technologies, Inc.
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Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

ANALYSIS OF FINANCIAL CONDITION

Excess acquisition cost as of September 30, 1998 was $94.8 million, an increase
of $18.4 million, compared with $76.4 million as of September 30, 1997. This
increase was due to an increase of $25.8 million primarily related to the impact
of businesses acquired in the fourth quarter of 1997, which was partially offset
by $7.1 million of amortized costs.

Other assets as of September 30, 1998 were $74.5 million, an increase of $25.4
million, compared with $49.1 million as of September 30, 1997. This increase was
primarily due to an increase of $23.1 million for patents, technology, formulas,
and covenants related to businesses acquired in the fourth quarter of 1997.

Accrued liabilities and taxes as of September 30, 1998 were $95.7 million, a
decrease of $12.7 million, compared with $108.4 million as of September 30,
1997. This decrease was primarily due to a decrease in accrued taxes of $9.2
million.

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 manufacture products, to 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 those 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 can be mitigated.

Project Plan

The Company's plan to resolve the year 2000 issue will be 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, risk assessment, prioritization, ownership assignment,
and compliance research phases, which are being performed concurrently, are
expected to be substantially completed by the end of 1998. The remediation and
testing phases are expected to be substantially completed by June 30, 1999 and
September 30, 1999, respectively. Although the Company's year 2000 plan is being
completed on a business by business basis, it is estimated that, overall, the
inventory and risk assessment phases are currently substantially complete, the
compliance research phase is approximately 50% to 60% complete, the remediation
phase is approximately 30% to 40% complete, and the testing phase is
approximately 20% to 30% complete.
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Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

IMPACT OF THE YEAR 2000, CONTINUED

The Company's year 2000 inventory is segregated into four categories: business
applications (mainframe/LAN software and desktop hardware/software), tools and
platforms (mainframe/LAN hardware), 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. Legacy systems for these businesses that
will not be replaced by the ERP system will either be made year 2000 compliant
or replaced. One business is in the process of "repairing" (i.e., making it year
2000 compliant) its existing core business system and will replace some portions
of its software with year 2000 compliant software. The remaining businesses have
upgraded their core business applications to a year 2000 compliant software
version and are in the process of testing these applications for year 2000
compliancy.

Non-IT systems are significantly more difficult to address than IT systems. The
Company has dedicated resources to assisting our businesses with identifying
potentially affected intelligent devices and has contracted with an outside firm
that has a proprietary year 2000 compliance status database that will assist in
the compliance research for these devices. Determination of compliance status,
remediation, and testing of these devices will also 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 will be
evaluated and, as deemed necessary, follow-up assessments will be made. We
expect this process to be ongoing throughout the remainder of 1998 and 1999.

Over the next several months, the Company will be developing detailed
contingency and business continuation plans for each business to address
potential year 2000 exposures.
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Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

IMPACT OF THE YEAR 2000, CONTINUED

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
$6.5 and $7.5 million and is being funded through operating cash flows. To date,
the Company has incurred approximately $2.1 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. 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, with the execution of
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 on 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.

IMPACT OF THE EURO CONVERSION

Within Europe, the European Economic and Monetary Union (the "EMU") will
introduce a new currency, the Euro, on January 1, 1999. The new currency is in
response to the EMU's policy of economic convergence to harmonize trade policy,
eliminate business costs associated with currency exchange, and to promote the
free flow of capital, goods, and services.

On January 1, 1999, the participating countries are scheduled to adopt the Euro
as their local currency, initially available for currency trading on currency
exchanges and non cash (banking) transactions. The existing local currencies, or
legacy currencies, will remain legal tender through January 1, 2002. Beginning
on January 1, 2002, Euro-denominated bills and coins will
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Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued

IMPACT OF THE EURO CONVERSION, CONTINUED

be issued for cash transactions. For a period of six months thereafter, both
legacy currencies and the Euro will be legal tender. On or before July 1, 2002,
the participating countries will withdraw all legacy currency and use the Euro
exclusively.

The Company has considered the effects of the Euro conversion on each of its
businesses and their systems and has determined that each business will be
capable of processing the necessary transactions in both Euro and legacy
currencies during this transition period. The Company has further determined
that its primary businesses operate in countries which are not deemed to be
"participating countries" at January 1, 1999, and therefore operations are not
expected to be materially affected by this conversion. The overall costs
associated with implementation of this conversion are not expected to be
material to the financial position, results of operations, and cash flows of the
Company as a whole.

FORWARD LOOKING STATEMENTS

Statements made in this report which 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, 1997.
<PAGE>   8
                                     PART II

                                OTHER INFORMATION


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 - Third 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>   9
                                   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)

     November 13, 1998                          /s/ Kathleen Burdett
Date...........................           ...................................

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




     November 13, 1998                           /s/ Glenn E. Tynan
Date...........................          ...................................

                                                 Glenn E. Tynan
                                                 Controller
                                                 (Principal Accounting Officer)
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                                INDEX TO EXHIBITS


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Exhibit No.
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<S>         <C>
    15      Letter to Securities and Exchange Commission re:  Incorporation
            of Accountants' Report

    27      Financial Data Schedule

    99      Third Quarter 1998 Financial Statements and Notes
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