<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:  MARCH 31, 1998

                                       OR

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

FOR THE TRANSITION PERIOD FROM ____________ TO ______________

COMMISSION FILE NUMBER:  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, 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 May 12, 1998

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<PAGE>   2




                       CAPSTEAD SECURITIES CORPORATION IV
                                    FORM 10-Q
                      FOR THE QUARTER ENDED MARCH 31, 1998


                                      INDEX

<TABLE>
<CAPTION>


                                                                                                             PAGE
                                                                                                             ---- 
                        PART I. -- FINANCIAL INFORMATION
<S>                                                                                                           <C>
ITEM 1. Financial Statements

   Balance Sheet -- March 31, 1998 and December 31, 1997..................................................    1

   Statement of Operations -- Quarter Ended March 31, 1998 and 1997.......................................    2

   Statement of Cash Flows -- Quarter Ended March 31, 1998 and 1997.......................................    3

   Notes to Financial Statements..........................................................................    4

ITEM 2. Management's Discussion and Analysis of
        Financial Condition and Results of Operations.....................................................    6


                          PART II. -- OTHER INFORMATION

ITEM 6. Exhibits and Reports on Form 8-K..................................................................    7

SIGNATURES................................................................................................    8
</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>

                                         MARCH 31, 1998   DECEMBER 31, 1997
                                         --------------   -----------------
                                          (UNAUDITED)
<S>                                        <C>             <C>      
ASSETS
   Mortgage securities collateral          $ 418,406       $ 493,147
   Cash and cash equivalents                   1,380               8
   Other assets                                1,313           1,508
                                           ---------       ---------

                                           $ 421,099       $ 494,663
                                           =========       =========

LIABILITIES
   Collateralized mortgage securities      $ 411,942       $ 485,633
   Accrued expenses                               43              40
                                           ---------       ---------

                                             411,985         485,673
                                           ---------       ---------

STOCKHOLDER'S EQUITY
   Common stock - $1.00 par value,
     1 shares authorized,
     issued and outstanding                        1               1
   Paid-in capital                             9,134           8,989
   Accumulated deficit                           (21)           --
                                           ---------       ---------

                                               9,114           8,990
                                           ---------       ---------

                                           $ 421,099       $ 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 MARCH 31
                                               ----------------------
                                                  1998        1997
                                               ---------    ---------
<S>                                             <C>          <C>    
Interest income:
   Mortgage securities collateral               $ 9,758      $15,748
   Receivable from Parent                             8           38
                                                -------      -------

     Total interest income                        9,766       15,786
                                                -------      -------

Interest expense on collateralized
   mortgage securities                            9,365       14,872
                                                -------      -------

       Net interest income                          401          914
                                                -------      -------

Other income - gain on sale of
   released mortgage securities collateral        1,557         --
                                                -------      -------

Other expenses:
   Management fees                                    3            3
   Professional fees and other                       28           37
   Pool insurance                                   307          515
                                                -------      -------

     Total other expenses                           338          555
                                                -------      -------

Net income                                        1,620          359
                                                -------      -------

Other comprehensive income                         --          2,153
                                                -------      -------

Comprehensive income                            $ 1,620      $ 2,512
                                                =======      =======

Net income per share                            $ 1,620      $   359

Number of share outstanding                           1            1

Cash dividends paid per share                   $ 1,641      $  --

</TABLE>



See accompanying notes to financial statements.


                                      -2-
<PAGE>   5


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


<TABLE>
<CAPTION>

                                                  QUARTER ENDED MARCH 31
                                                  -----------------------
                                                    1998           1997
                                                  ---------      --------
<S>                                               <C>            <C>     
OPERATING ACTIVITIES:
   Net income                                     $  1,620       $    359
   Noncash item - amortization of
     discount and premium                              273            143
   Net change in other assets and
     accrued expenses                                  198            281
   Gain on sale of released mortgage
     securities collateral                          (1,557)          --
                                                  --------       --------
         Net cash provided by operating
           activities                                  534            783
                                                  --------       --------

INVESTING ACTIVITIES:
   Mortgage securities collateral:
     Principal collections on collateral            42,178         35,169
     Decrease in accrued interest receivable           576            259
     Increase in short-term investments             (3,209)        (1,555)
   Sale of released mortgage securities
     collateral                                     37,048           --
                                                  --------       --------
         Net cash provided by
           investing activities                     76,593         33,873
                                                  --------       --------

FINANCING ACTIVITIES:
   Collateralized mortgage securities:
     Principal payments on securities              (73,483)       (33,285)
     Decrease in accrued interest payable             (776)          (367)
   Capital contributions (distributions)               145         (3,635)
   Dividends paid                                   (1,641)          --
                                                  --------       --------
         Net cash used by
           financing activities                    (75,755)       (37,287)
                                                  --------       --------

Net change in cash and cash equivalents              1,372         (2,631)

Cash and cash equivalents at beginning
   of period                                             8          2,675
                                                  --------       --------                        
Cash and cash equivalents at end of
   period                                         $  1,380       $     44
                                                  ========       ========
</TABLE>




See accompanying notes to financial statements.

                                      -3-

<PAGE>   6


                       CAPSTEAD SECURITIES CORPORATION IV
                          NOTES TO FINANCIAL STATEMENTS
                                 MARCH 31, 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 ended March 31, 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. Currently, 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. There were no
securities classified as available-for-sale at December 31, 1997, as the final
such security was sold during April 1997. 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 table summarizes fair value disclosures for mortgage securities 
collateral (in thousands):

<TABLE>
<CAPTION>

                                    MARCH 31, 1998  DECEMBER 31, 1997
                                    --------------  -----------------

<S>                                     <C>            <C>      
         Carrying amount                $ 418,406      $ 493,147
         Unrealized gains                  11,333         13,280
         Unrealized losses                   (144)         (158)
                                        ---------      ---------

           Fair value                   $ 429,595      $ 506,269
                                        =========      =========
</TABLE>


All mortgage securities collateral is held-to-maturity. 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 table summarizes disclosures related to the disposition of
released CMO collateral held-to-maturity at March 31, 1998 (in thousands):

<TABLE>
<CAPTION>
                                             COST BASIS                GAINS
                                             ----------                ------
<S>                                           <C>                      <C>   
CMO Series 1991-VII                           $35,076                  $1,557
</TABLE>

NOTE C -- NET INTEREST INCOME ANALYSIS

The following table summarizes 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 MARCH 31
                                       ---------------------------------------------------- 
                                               1998                            1997
                                       ---------------------           --------------------
                                                    AVERAGE                         AVERAGE
                                        AMOUNT       RATE              AMOUNT         RATE
                                        ------      -------            -------      -------
<S>                                     <C>          <C>               <C>            <C>  
Interest income on mortgage
   securities collateral                $9,758       8.33%             $15,748        8.52%
Interest expense on
   collateralized mortgage
   securities                            9,365       8.17               14,872        8.19
                                        ------                         -------

Net interest                            $  393                         $   876
                                        ======                         =======
</TABLE>

The following table summarizes the amount of change in interest income and
interest expense due to changes in effective interest rates versus changes in
volume (in thousands):

<TABLE>
<CAPTION>
   
                                                RATE*               VOLUME*                TOTAL
                                               --------             ---------            ---------   
<S>                                             <C>                 <C>                   <C>     
Interest income on mortgage
   securities collateral                        $(333)              $(5,657)              $(5,990)
Interest expense on
   collateralized mortgage securities             (40)               (5,467)               (5,507)
                                                -----               -------               -------

                                                $(293)              $  (190)              $  (483)
                                                =====               =======               =======
</TABLE>

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


                                      -5-
<PAGE>   8


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 March 31, 1998, the Company has issued 18 CMOs with an
aggregate initial principal balance of $4,226,812,000, 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 CMOs (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 $58,000 for
the quarter ended March 31, 1998, compared to $324,000 for the same period in
1997. Operating results produced by CMO Investments are 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 19 basis
point decrease in collateral yields and a 37% decrease in the average holdings
of mortgage securities collateral during the first quarter of 1998 compared to
the same period in 1997. This was a result of run-off (prepayments and scheduled
payments) and the redemption of CMO Series 1991-VII during the first quarter of
1998. Average holdings of mortgage securities collateral were $468 million for
the quarter ended March 31, 1998, compared to $740 million for the corresponding
prior year period. As a result of lower outstanding balances, income earned from
the net interest spread was lower in the current quarter. The run-off rate was
36% during the quarter ended March 31, 1998, compared to 19% during the same
period in 1997.

The following table presents the weighted average yields for the periods shown:

<TABLE>
<CAPTION>
                                                     QUARTER ENDED MARCH 31
                                                    -----------------------
                                                    1998               1997
                                                    ----               ----
<S>                                                 <C>                <C>  
     Mortgage securities collateral                 8.33%              8.52%
     Collateralized mortgage securities             8.17               8.19
                                                    ----               ----

     Net margin                                     0.16%              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, four CMOs were redeemed between March 31,
1997 and March 31, 1998. Three of these Series had 



                                       -6-

<PAGE>   9

collateral yielding in excess of 8.50%, contributing 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. 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:  None.

        Exhibit 27 Financial Data Schedule (electronic filing only).

(b)     Reports on Form 8-K:  None.





                                      -7-
<PAGE>   10


                                   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:  May 12, 1998                 By: /s/ RONN K. LYTLE
                                       -------------------------------------
                                       Ronn K. Lytle
                                       Chairman and Chief Executive Officer



Date:  May 12, 1998                 By: /s/ JULIE MOORE
                                       -------------------------------------
                                       Julie Moore
                                       Senior Vice President - Control
                                         and Treasurer


                                      -8-
<PAGE>   11

                                 EXHIBIT INDEX

<TABLE>
<CAPTION>

EXHIBIT 
  NO.               DESCRIPTION
-------             -----------

<S>                 <C>
27                  Financial Data Schedule 
</TABLE>