<PAGE>   1
                     SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C.  20549
                                -------------

                                  FORM 10-Q

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

                For the quarterly period ended March 31, 1997

                       Commission file number 0-10810

                            KIEWIT ROYALTY TRUST
   ----------------------------------------------------------------------
           (Exact Name of Registrant as Specified in Its Charter)


<TABLE>
<S>                                                                 <C>
            Nebraska                                                            47-6131402              
------------------------------------                                ------------------------------------
(State or Other Jurisdiction of                                     (I.R.S. Employer Identification No.)
 Incorporation or Organization)
</TABLE>


                       First Bank, National Association
                              1700 Farnam Street
                            Omaha, Nebraska  68102
                   ---------------------------------------
                   (Address of Principal Executive Offices)

      Registrant's Telephone Number, Including Area Code: (402) 348-6000



                 Indicate by check X 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 
                                                ------    ------  

                 As of May 14, 1997, there were 12,633,432 Units of Beneficial
Interest of the registrant outstanding.





                                       
<PAGE>   2
                                     PART I
                             FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS.

                              KIEWIT ROYALTY TRUST
               STATEMENT OF ASSETS, LIABILITIES AND TRUST CORPUS
                   as of March 31, 1997 and December 31, 1996

<TABLE>
<CAPTION>
ASSETS                                           1997                              1996
------                                           ----                              ----
<S>                                        <C>                               <C>
Cash and short-term investments            $     1,851,559                   $       244,268

Royalty and overriding
royalty interests in coal leases           $       167,817                   $       167,817

Less accumulated amortization              $       (77,805)                  $       (76,921)

Net royalty and overriding
royalty interests in coal leases           $        90,012                   $        90,896
                                           ----------------                  ----------------

TOTAL ASSETS                               $     1,941,571                   $       335,164
                                           ================                  ================


LIABILITIES AND TRUST CORPUS
----------------------------

Distributions payable to Unit Holders      $     1,851,559                   $       244,268

Trust Corpus:  12,633,432
Units of Beneficial Interest
authorized and outstanding                 $        90,012                   $        90,896
                                           ----------------                  ----------------

Total Liabilities and Trust Corpus         $     1,941,571                   $       335,164
                                           ================                  ================
</TABLE>




                  The accompanying notes are an integral part
                          of the financial statements.





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<PAGE>   3
                              KIEWIT ROYALTY TRUST

                       STATEMENT OF DISTRIBUTABLE INCOME
               for the Three Months Ended March 31, 1997 and 1996

<TABLE>
<CAPTION>
                                                                Three Months
                                                                Ended March 31
                                                                --------------

                                                  1997                               1996
                                                  ----                               ----
<S>                                        <C>                               <C>
Royalty Income                             $       1,850,105                 $       2,243,681

Interest Income                            $          16,342                 $          23,206

Trust Expenses                             $         (14,888)                $         (15,518)
                                           ------------------                ------------------

Distributable Income                       $       1,851,559                 $       2,251,369

Distributable Income per Unit
(12,633,432 Units Outstanding)                     0.1465603                         0.1782072
</TABLE>



                      STATEMENT OF CHANGES IN TRUST CORPUS
               for the Three Months Ended March 31, 1997 and 1996

<TABLE>
<CAPTION>
                                                                 Three Months
                                                                Ended March 31
                                                                --------------

                                                          1997                       1996
                                                          ----                       ----
<S>                                            <C>                           <C>
Trust Corpus as of January 1                   $         90,896              $        96,920
                                                                
Amortization of Royalty Interest               $           (884)             $        (3,071)
                                                                
Distributable Income                           $      1,851,559              $     2,251,369
                                                                
Distribution to Unit Holders                   $     (1,851,559)             $    (2,251,369)
                                               ----------------              ---------------
                                                                
Trust Corpus as of March 31                    $         90,012              $        93,849
                                               ================             ================
</TABLE>




                See accompanying Notes to Financial Statements.





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<PAGE>   4
                              KIEWIT ROYALTY TRUST

                         Notes to Financial Statements
                   as of March 31, 1997 and December 31, 1996

Basis of Presentation

                 The accompanying unaudited financial statements have been
prepared in accordance with the instructions for Form 10-Q and do not
necessarily include all of the information and footnotes required by generally
accepted accounting principles for complete financial statements.  In the
Trustee's opinion, all adjustments necessary for a fair presentation have been
included.  For further information, refer to the financial statements and
footnotes included in the Trust's annual report on Form 10-K for the year ended
December 31, 1996.

Summary of Significant Accounting Policies

                 The accompanying unaudited financial statements have been
prepared on the following basis:

                 (a)      The royalty income recorded for a month is the amount
                          computed and paid by the lease holder to the Trustee
                          for such month.

                 (b)      Trust administration expenses are recorded in the
                          month they accrue.

This basis for reporting royalty income is thought to be the most meaningful
because distributions to the Unit Holders for a month are based on net cash
receipts for such month.  However, these statements differ from financial
statements prepared in accordance with generally accepted accounting principles
because, under such principles, royalty income for a month would be based on
production for such month without regard to when calculated or received.  In
addition, amortization of the net royalty and overriding royalty interests,
which is calculated on a units- of-production basis by lease, is charged
directly to trust corpus, since such amount does not affect distributable
income.





                                       -4-
<PAGE>   5
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
         RESULTS OF OPERATIONS.

         a.      Material Changes in Financial Condition.

                 Kiewit Royalty Trust is a royalty trust with royalty and
overriding royalty interests in certain coal leases.  The Trust was formed for
the purposes of (1) administering the income received from such coal leases and
(2) distributing such income (together with interest earned thereon less
payment of or provision for obligations) to the holders of the Units of
Beneficial Interest.

         b.      Material Changes in Results of Operations.

                 During the first quarter of 1997, the Trust received a total
$1,850,105 of royalty and overriding royalty payments.  The following schedule
reflects the royalty and overriding royalty amounts received by the Trust from
each mine for the three months ended March 31, 1997 and 1996.

<TABLE>
<CAPTION>
                 Mine                                First Quarter
                 ----                                -------------
                                           1997                      1996
                                           ----                      ----
                 <S>                   <C>                       <C>
                 Decker                $1,837,048                 $2,104,649
                 Big Horn                  13,057                      1,493
                 Black Butte                ---                      137,539
                 Spring Creek               ---                       ---   
                                       ----------                 ----------
                                       $1,850,105                 $2,243,681
                                       ==========                 ==========
</TABLE>


                 i.       Decker Mine.

                 The amount of royalties and overriding royalties received by
the Trust with respect to the Decker Mine decreased to $1,837,048 in the first
quarter of 1997 compared to $2,104,649 during the same period in 1996. The
decrease for the first quarter of 1997 was due to changes in the relative
amounts of coal mined under leases bearing high and low overriding royalty
rates per ton, which are a normal result of the execution of a mining plan
encompassing several coal leases bearing different royalty rates and decreased
production from the applicable leases.

                 ii.      Big Horn Mine.

                 Royalties received from the Big Horn Mine increased to $13,057
during the first quarter of 1997 from $1,493 in 1996.  This increase reflects
increased production from the applicable lease.





                                       -5-
<PAGE>   6
                 iii.     Black Butte Mine.

                 The Trust received no royalties from the Black Butte Mine
during the first quarter of 1997, as compared to $137,539 during the first
quarter of 1996.  The decrease in royalties received during the first quarter
of 1997 reflects the fact that Federal Lease number W-6266 was renewed
effective April 1, 1996, and the Trust no longer receives an overriding royalty
on coal produced after March 31, 1996, as explain below.

                 Lease number W-6266 provides that the terms and conditions of
the lease are subject to "reasonable readjustment" effective on April 1, 1996.
At that time, the royalty rate payable to the United States was increased to
12-1/2%, which is the currently prevailing federal royalty rate.  Because of
the cap on the amount of the overriding royalty payable to the Trust with
respect to this lease, the increased royalty rate has effectively eliminated
further payments to the Trust with respect to this lease.

                 iv.      Spring Creek Mine.

                 No royalties were received from the Spring Creek Mine during
the first quarters of 1997 or 1996 because royalties are typically paid by the
mine operators on an annual basis during the second half of a calendar year.

                                    PART II
                               OTHER INFORMATION

ITEM 1.  LEGAL PROCEEDINGS.

         There are no material pending legal proceedings to which the Trust is
a party or of which any of its property is the subject.

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

         (a)     Exhibits.

                 27.1     Financial Data Schedule.

         (b)     No reports on Form 8-K were filed during the quarter for which
                 this report is filed.





                                       -6-
<PAGE>   7
                                   SIGNATURE

                 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.

Date: May 14, 1997             KIEWIT ROYALTY TRUST
                               --------------------
                                        (Registrant)
                               
                               By:      First Bank, National Association, in 
                                        its capacity as Trustee and not in
                                        its individual capacity or otherwise
                               
                               
                               
                                        By  /s/   Susan K. Rosburg             
                                           ------------------------------------
                                                Susan K. Rosburg
                                                Trust Officer





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