<PAGE>   1

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                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 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:  33-42337

                       CAPSTEAD SECURITIES CORPORATION IV
             (Exact name of Registrant as specified in its Charter)

          DELAWARE                                             75-2390594
(State or other jurisdiction of                             (I.R.S. Employer
 incorporation or organization)                            Identification No.)

2711 NORTH HASKELL AVENUE, DALLAS, TEXAS                         75204
(Address of principal executive offices)                      (Zip Code)

        Registrant's telephone number, including area code (214) 874-2323


The Registrant meets the conditions set forth in General Instruction H(1)(a) and
(b) for Form 10-Q and is therefore filing this Form under the reduced disclosure
format.

Indicate by check mark whether the Registrant (1) has filed all documents and
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
                                              ---   ---

                      APPLICABLE ONLY TO CORPORATE ISSUERS:

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

Common Stock ($1.00 par value)                     1,000 as of November 3, 1998

================================================================================

<PAGE>   2

                       CAPSTEAD SECURITIES CORPORATION IV
                                    FORM 10-Q
                    FOR THE QUARTER ENDED SEPTEMBER 30, 1998


                                      INDEX

<TABLE>
<CAPTION>

                                                                                                             PAGE
                        PART I. -- FINANCIAL INFORMATION                                                     ----

ITEM 1. Financial Statements
<S>                                                                                                           <C>
   Balance Sheet -- September 30, 1998 (Unaudited)
     and December 31, 1997................................................................................    1

   Statement of Operations -- Quarter and Nine Months Ended
     September 30, 1998 and 1997 (Unaudited)..............................................................    2

   Statement of Cash Flows -- Nine Months Ended
     September 30, 1998 and 1997 (Unaudited)..............................................................    3

   Notes to Financial Statements (Unaudited)..............................................................    4

ITEM 2.       Management's Discussion and Analysis of
              Financial Condition and Results of Operations...............................................    7


                          PART II. -- OTHER INFORMATION

ITEM 6.       Exhibits and Reports on Form 8-K............................................................    8

SIGNATURES................................................................................................    9
</TABLE>


<PAGE>   3



                        PART I. -- FINANCIAL INFORMATION
                       CAPSTEAD SECURITIES CORPORATION IV
                                  BALANCE SHEET
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)


ITEM 1. FINANCIAL STATEMENTS

<TABLE>
<CAPTION>

                                                SEPTEMBER 30, 1998          DECEMBER 31, 1997
                                                ------------------          -----------------
                                                 (UNAUDITED)

ASSETS
<S>                                                <C>                         <C>     
   Mortgage securities collateral                  $617,029                    $493,147
   Cash and cash equivalents                            189                           8
   Other assets                                         824                       1,508
                                                   --------                    --------

                                                   $618,042                    $494,663
                                                   ========                    ========

LIABILITIES
   Collateralized mortgage securities              $612,766                    $485,633
   Accrued expenses                                      48                          40
   Payable to Parent                                  1,136                           -
                                                   --------                    --------

                                                    613,950                     485,673
                                                   --------                    --------

STOCKHOLDER'S EQUITY
   Common stock - $1.00 par value,
     1 shares authorized,
     issued and outstanding                               1                           1
   Paid-in capital                                    4,091                       8,989
   Undistributed income                                   -                           -
                                                   --------                    --------

                                                      4,092                       8,990
                                                   --------                    --------

                                                   $618,042                    $494,663
                                                   ========                    ========
</TABLE>


See accompanying notes to financial statements.

                                      -1-
<PAGE>   4



                       CAPSTEAD SECURITIES CORPORATION IV
                             STATEMENT OF OPERATIONS
                                   (UNAUDITED)
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>

                                            QUARTER ENDED            NINE MONTHS ENDED
                                            SEPTEMBER 30               SEPTEMBER 30
                                        ---------------------     ---------------------
                                          1998         1997        1998          1997
                                        --------     --------     --------     --------
<S>                                     <C>          <C>          <C>          <C>     
Interest income:
   Mortgage securities collateral       $  6,352     $ 11,990     $ 23,999     $ 41,409
   Receivable from Parent                     20           17           50           60
                                        --------     --------     --------     --------

     Total interest income                 6,372       12,007       24,049       41,469
                                        --------     --------     --------     --------

Interest expenses on collateralized
   mortgage securities                     6,069       11,485       23,289       39,033
                                        --------     --------     --------     --------

       Net interest income                   303          522          760        2,436
                                        --------     --------     --------     --------

Other income - gain on sale of
   released mortgage securities
   collateral                              1,331         --          2,888        2,794
                                        --------     --------     --------     --------

Other expenses:
   Management fees                             3            3            8            8
   Professional fees and other                19           19           69           85
   Pool insurance                            228          353          794        1,283
                                        --------     --------     --------     --------

     Total other expenses                    250          375          871        1,376
                                        --------     --------     --------     --------

Net income                                 1,384          147        2,777        3,854

Other comprehensive loss                    --           --           --         (2,646)
                                        --------     --------     --------     --------

Comprehensive income (loss)             $  1,384     $    147     $  2,777     $  1,208
                                        ========     ========     ========     ========
</TABLE>

See accompanying notes to financial statements.

                                      -2-
<PAGE>   5



                       CAPSTEAD SECURITIES CORPORATION IV
                             STATEMENT OF CASH FLOWS
                                   (UNAUDITED)
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>

                                            NINE MONTHS ENDED SEPTEMBER 30
                                                1998           1997
                                             ---------      ---------
<S>                                           <C>                <C>  
OPERATING ACTIVITIES:
   Net income                                 $   2,777          3,854
   Noncash item - amortization of
     discount and premium                           996            580
   Net change in other assets and
     accrued expenses                               692            869
   Gain on sale of released mortgage
     securities collateral                       (2,888)        (2,794)
                                              ---------      ---------
         Net cash provided by operating
           activities                             1,577          2,509
                                              ---------      ---------

INVESTING ACTIVITIES:
   Mortgage securities collateral:
     Purchases of collateral                   (353,442)          --
     Principal collections on collateral        141,375         97,900
     Decrease (increase) in accrued
       interest receivable                         (625)         1,470
     Decrease (increase) in short-term
       investments                                5,069         (1,537)
   Sale of released mortgage
     securities collateral                       87,216        117,261
                                              ---------      ---------
         Net cash provided (used) by
           investing activities                (120,407)       215,094
                                              ---------      ---------

FINANCING ACTIVITIES:
   Collateralized mortgage securities:
     Issuance of securities                     355,568
     Principal payments on securities          (227,271)      (209,767)
     Decrease in accrued interest payable        (2,747)        (1,895)
   Increase in payable to Parent                  1,136           --
   Capital distributions                         (4,898)        (7,734)
   Dividends paid                                (2,777)          (813)
                                              ---------      ---------
         Net cash provided (used) by
           financing activities                 119,011       (220,209)
                                              ---------      ---------

Net change in cash and cash equivalents             181         (2,606)

Cash and cash equivalents at beginning
   of period                                          8          2,675
                                              ---------      ---------

Cash and cash equivalents at end of
   period                                     $     189      $      69
                                              =========      =========
</TABLE>


See accompanying notes to financial statements.

                                      -3-
<PAGE>   6



                       CAPSTEAD SECURITIES CORPORATION IV
                          NOTES TO FINANCIAL STATEMENTS
                               SEPTEMBER 30, 1998
                                   (UNAUDITED)



NOTE A -- BASIS OF PRESENTATION

The accompanying unaudited financial statements have been prepared in accordance
with generally accepted accounting principles for interim financial information
and with the instructions to Form 10-Q and Rule 10-01 of Regulation S-X.
Accordingly, they do not include all of the information and footnotes required
by generally accepted accounting principles for complete financial statements.
In the opinion of management, all adjustments (consisting of normal recurring
accruals) considered necessary for a fair presentation have been included.
Operating results for the quarter and nine months ended September 30, 1998 are
not necessarily indicative of the results that may be expected for the calendar
year ending December 31, 1998. For further information refer to the financial
statements and footnotes thereto included in the Capstead Securities Corporation
IV (the "Company") annual report on Form 10-K for the year ended December 31,
1997.

On January 1, 1997 the Company adopted Statement of Financial Accounting
Standards No. 130, "Reporting Comprehensive Income" ("SFAS 130"). SFAS 130
establishes standards for the reporting of comprehensive income and its
components in financial statements. As the term relates to the Company,
comprehensive income consists of net income plus the change in unrealized gains
and losses on debt securities classified as available-for-sale that is included
as a component of stockholders' equity. The adoption of SFAS 130 has not had any
impact on the results of operations or financial position of the Company.

NOTE B -- DISCLOSURES REGARDING FAIR VALUES OF MORTGAGE SECURITIES COLLATERAL

The estimated fair values of mortgage securities collateral have been determined
using available market information and appropriate valuation methodologies.
However, considerable judgment is required in interpreting market data to
develop these estimates. In addition, fair values fluctuate on a daily basis.
Accordingly, estimates presented herein are not necessarily indicative of the
amounts that could be realized in a current market exchange. The use of
different market assumptions and/or estimation methodologies may have a material
effect on estimated fair value amounts.

Fair values are estimated using quoted market prices, when available, including
quotes made by Capstead Mortgage Corporation's lenders in connection with
designating collateral for repurchase arrangements.


                                      -4-
<PAGE>   7



The following tables summarize fair value disclosures for mortgage securities
collateral held available-for-sale and held-to-maturity for the periods
indicated (in thousands):
<TABLE>
<CAPTION>

                                             AS OF  SEPTEMBER 30, 1998
                             -------------------------------------------------------------
                                              GROSS            GROSS
                                            UNREALIZED       UNREALIZED             FAIR
                               COST           GAINS            LOSSES               VALUE
                             --------         ------            ----              --------
<S>                          <C>              <C>               <C>               <C>     
Available-for-sale           $355,725         $    -            $  -              $355,725
Held-to-maturity              261,304          7,362             105               268,561
                             --------         ------            ----              --------
                             $617,029         $7,362            $105              $624,286
                             ========         ======            ====              ========
<CAPTION>

                                             AS OF  DECEMBER 31, 1997
                             -------------------------------------------------------------
                                              GROSS            GROSS
                                            UNREALIZED       UNREALIZED            FAIR
                                COST          GAINS            LOSSES              VALUE
                             --------         ------            ----              --------
<S>                          <C>             <C>                <C>               <C>     
Held-to-maturity             $493,147        $13,280            $158              $506,269
                             ========        =======            ====              ========
</TABLE>

The maturity of mortgage securities collateral is directly affected by the rate
of principal prepayments by mortgagors. In addition, upon redemption of
remaining bonds outstanding pursuant to clean-up calls, released collateral may
be sold. Such sales are deemed maturities under the provisions of Statement of
Financial Accounting Standards No. 115.

The following tables summarize disclosures related to the disposition of
released CMO collateral held-to-maturity (in thousands):
<TABLE>
<CAPTION>

                                                           QUARTER ENDED             NINE MONTHS ENDED
                                                            SEPTEMBER 30                SEPTEMBER 30
                                                         -------------------       ----------------------
                                                          1998         1997         1998             1997
                                                         -------       ----        -------         ------
<S>                                                     <C>            <C>         <C>           <C>     
Sale of released CMO collateral held-to-maturity:
     Amortized cost                                     $48,836        $ -         $84,328       $114,468
     Gains                                                1,331          -           2,888          2,794
</TABLE>

NOTE C -- MORTGAGE SECURITIES COLLATERAL

On September 29, 1998 the Company acquired from its affiliates AAA-rated private
mortgage pass-through certificates backed by conventional mortgage loans with
unpaid principal balances of $345.8 million that were pledged as collateral for
the immediate issuance of CMO Series 1998-III. These mortgage pass-through
certificates were obtained at an amount equal to the net proceeds of the
issuance.

NOTE D -- COLLATERALIZED MORTGAGE SECURITIES

On September 29, 1998 the Company issued collateralized mortgage securities (CMO
Series 1998-III) with a 26 year stated maturity and a total obligation
(including accrued interest and premium) of $355.7 million. The Company retained
no beneficial interest in this CMO and as such, no economic benefit will be
received and no related net income or loss will be recognized other than the
amortization of unreimbursed shelf issuance costs totaling $42,000. This issue
is callable on or after March 25, 2001. The interest-only 


                                      -5-
<PAGE>   8

securities issued in connection with this CMO totaling $10.3 million were
acquired by an affiliate of the Company.

NOTE E -- NET INTEREST INCOME ANALYSIS

The following tables summarize the amount of interest income and interest
expense and the average effective interest rates for mortgage securities
collateral and collateralized mortgage securities (dollars in thousands):
<TABLE>
<CAPTION>

                                                   QUARTER ENDED SEPTEMBER 30
                                     ----------------------------------------------------
                                            1998                           1997
                                     --------------------          ----------------------
                                                 AVERAGE                          AVERAGE
                                     AMOUNT        RATE            AMOUNT           RATE
                                     ------       -----            ------         -------
<S>                                  <C>          <C>              <C>             <C>  
Interest income on mortgage
   securities collateral             $6,352       8.29%            $11,990         8.50%
Interest expense on
   collateralized mortgage
   securities                         6,069       8.10              11,485         8.32
                                     ------                        -------
Net interest                         $  283                        $   505
                                     ======                        =======
</TABLE>

<TABLE>
<CAPTION>

                                                NINE MONTHS ENDED SEPTEMBER 30
                                     ----------------------------------------------------
                                            1998                           1997
                                     --------------------          ----------------------
                                                 AVERAGE                          AVERAGE
                                     AMOUNT       RATE             AMOUNT          RATE
                                     ------       -----            ------         -------
<S>                                 <C>           <C>              <C>             <C>  
Interest income on mortgage
   securities collateral            $23,999       8.25%            $41,409         8.49%
Interest expense on
   collateralized mortgage
   securities                        23,289       8.18              39,033         8.16
                                    -------                        -------
Net interest                        $   710                        $ 2,376
                                    =======                        =======
</TABLE>

The following tables summarize changes in interest income and interest expense
due to changes in effective interest rates, versus changes in volume for the
quarter and nine months ended September 30, 1998, compared to the same periods
in 1997 (in thousands):
<TABLE>
<CAPTION>

                                                      QUARTER ENDED SEPTEMBER 30, 1998
                                                 --------------------------------------
                                                  RATE*        VOLUME*          TOTAL
                                                 -------       --------        --------
<S>                                              <C>           <C>             <C>      
Interest income on mortgage
   securities collateral                          $(285)       $(5,353)        $(5,638)
Interest expense on
   collateralized mortgage securities              (290)        (5,126)         (5,416)
                                                  -----        -------         -------
                                                  $   5        $  (227)        $  (222)
                                                  =====        =======         =======
<CAPTION>

                                                   NINE MONTHS ENDED SEPTEMBER 30, 1998
                                                 --------------------------------------
                                                  RATE*         VOLUME*          TOTAL
                                                 -------       --------        --------
<S>                                              <C>           <C>             <C>      
Interest income on mortgage
   securities collateral                         $(1,131)      $(16,279)       $(17,410)
Interest expense on
   collateralized mortgage securities                100        (15,844)        (15,744)
                                                 -------       --------        --------
                                                 $(1,231)      $   (435)       $ (1,666)
                                                 =======       ========        ========
</TABLE>

*    THE CHANGES IN INTEREST INCOME AND EXPENSE DUE TO BOTH VOLUME AND RATE HAVE
     BEEN ALLOCATED TO VOLUME AND RATE CHANGES IN PROPORTION TO THE RELATIONSHIP
     OF THE ABSOLUTE DOLLAR AMOUNTS OF THE CHANGE IN EACH.

                                      -6-
<PAGE>   9



ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
         RESULTS OF OPERATIONS

FINANCIAL CONDITION

Capstead Securities Corporation IV (the "Company") was incorporated on August
16, 1991, as a special-purpose finance subsidiary of Capstead Mortgage
Corporation ("CMC") and commenced operations on December 23, 1991 with the
issuance of its first collateralized mortgage obligation ("CMO"), Series
1991-VIII. As of September 30, 1998, the Company had issued 19 CMOs with an
aggregate initial principal balance of $4,572,644,000, including two CMOs with
an aggregate initial principal balance of $551,537,000, which were recorded as
sales when issued in 1992.

RESULTS OF OPERATIONS

Residual investments in collateralized mortgage obligations (represented by the
difference between the carrying value of mortgage securities collateral and
collateralized mortgage securities on the balance sheet; also referred to as
"CMO Investments") earned $36,000 and recorded a loss of $153,000 for the
quarter and nine months ended September 30, 1998, respectively, compared to
earning $133,000 and $1,008,000 for the same periods in 1997. Operating results
produced by CMO Investments is represented by the difference between interest
income on mortgage securities collateral and interest expense and professional
fees on collateralized mortgage securities and mortgage pool insurance expense
on mortgage securities collateral.

Operating results from CMO Investments declined due primarily to a 40% decrease
in the average holdings of mortgage securities collateral during the nine months
ended September 30, 1998 compared to the same period in 1997. Average holdings
of mortgage securities collateral were $306 million and $388 million during the
quarter and nine months ended September 30, 1998, respectively, compared to $564
million and $651 million for the corresponding prior year periods. The decreases
in average holdings were the result of run-off (prepayments and scheduled
payments) and the redemptions of five CMOs during the 12 months ended September
30, 1998. The run-off rate was 40% during the nine months ended September 30,
1998, compared to 17% during the same period in 1997. As a result of lower
outstanding balances, income earned from the net interest spread was lower
during 1998.

The following tables present the weighted average yields for the periods shown:
<TABLE>
<CAPTION>

                                        QUARTER ENDED      NINE MONTHS ENDED
                                        SEPTEMBER 30        SEPTEMBER 30
                                       ---------------     --------------
                                       1998      1997      1998      1997
                                       -----     -----     -----     ----
<S>                                    <C>       <C>       <C>       <C>  
Mortgage securities collateral         8.29%     8.50%     8.25%     8.49%
Collateralized mortgage securities     8.10      8.32      8.18      8.16
                                       ----      ----      ----      ----

Net interest spread                    0.19%     0.18%     0.07%     0.33%
                                       ====      ====      ====      ====
</TABLE>

Although net margins can fluctuate depending on the timing of the payoff of
collateral and bonds with differing amounts of purchase premium and bond
discounts, the tendency is for CMO net margins to decline as lower-yielding,
shorter-term CMO bonds are paid off prior to longer-term bonds with relatively
higher interest rates. Additionally, five CMOs were redeemed 


                                      -7-
<PAGE>   10

between September 30, 1997 and September 30, 1998, including 1992-X which was
recorded as a sale when issued. These CMOs had collateral yielding between 8.62%
and 9.23% at the time of redemption, which contributed to the decline in average
collateral yields.

LIQUIDITY AND CAPITAL RESOURCES

The Company's primary sources of funds are the receipt of excess cash flows on
CMO Investments (primarily the excess of principal and interest earned on the
mortgage securities collateral including reinvestment proceeds over the
principal and interest payable on the CMOs), proceeds from additional CMO
issuances and occasionally proceeds from the sale of collateral released from
the related CMOs. During the first quarter of 1998, the Company redeemed the
remaining outstanding bonds of CMO Series 1991-VII totaling $35,922,000 pursuant
to clean-up calls, and sold the related released collateral of $35,492,000 for a
gain of $1,557,000. During the third quarter of 1998, the Company redeemed the
remaining outstanding bonds of CMO Series 1992-V and 1992-VII totaling
$53,648,000 pursuant to clean-up calls, and sold the related released collateral
of $48,836,000 for a gain of $1,331,000. The Company continues to qualify as a
real estate investment trust subsidiary.


                          PART II. -- OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K:

(a)     Exhibits:

        Exhibit 27 - Financial Data Schedule (electronic filing only).

(b)     Reports on Form 8-K:

        Current Report on Form 8-K dated September 30, 1998 to file the
        following:

        Exhibit 99.1 - Computational Materials Provided by Greenwich Capital 
        Markets, Inc.

        Current Report on Form 8-K dated September 28, 1998 to file the
        following:

        Exhibits 5.1 and 8.1 - Opinion of Andrews & Kurth, LLP.

        Exhibit 24.1 - Consent of Andrews & Kurth, LLP.

                                      -8-
<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.


                                           CAPSTEAD SECURITIES CORPORATION IV





Date:  November 3, 1998                    By: /s/ RONN K. LYTLE
                                               --------------------------------
                                               Ronn K. Lytle
                                               Chairman and Chief Executive 
                                                  Officer




Date:  November 3, 1998                    By: /s/ ANDREW F. JACOBS
                                               --------------------------------
                                               Andrew F. Jacobs
                                               Executive Vice President - 
                                                  Finance, Treasurer and 
                                                  Secretary

                                      -9-
<PAGE>   12



                                 EXHIBIT INDEX

EXHIBIT             DESCRIPTION
-------             -----------
 27                 Financial Date Schedule