<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

[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 1-8971

                                   RCPI Trust
             (Exact name of registrant as specified in its charter)

           Delaware                                              13-7087445
(State or other jurisdiction of                               (I.R.S. Employer
incorporation or organization)                               Identification No.)

                       c/o Tishman Speyer Properties, L.P.
                   45 Rockefeller Plaza, New York, N.Y. 10011
               (Address of principal executive offices) (Zip Code)


                                 (212) 332-6500
              (Registrant's telephone number, including area code)

________________________________________________________________________________
   (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 _____
<PAGE>   2
                                   RCPI TRUST


INDEX

                                                                            PAGE
PART I--FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS

The accompanying unaudited, interim financial statements have been
prepared in accordance with the instructions to Form 10-Q. In the opinion
of management, all adjustments necessary for a fair presentation have been
included.

         RCPI Trust, Balance Sheets as of March 31, 1998 (unaudited) and
         December 31, 1997                                                     1

         RCPI Trust, Statements of Operations for the quarters ended March 
         31, 1998 and 1997 (unaudited)                                         2

         RCPI Trust, Statements of Cash Flows for the quarters ended March 
         31, 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                                                 5


PART II--OTHER INFORMATION


ITEM 1.  LEGAL PROCEEDINGS                                                     8

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K                                      9
<PAGE>   3
PART I -- FINANCIAL INFORMATION
       ITEM 1.  Financial Statements


                                   RCPI TRUST
                           (A Delaware business trust)
                                 BALANCE SHEETS
                   AS OF MARCH 31, 1998 AND DECEMBER 31, 1997
                                ($ in thousands)


<TABLE>
<CAPTION>
                                                                       March 31, 1998
                                                                         (Unaudited)   December 31, 1997
                                                                          ---------        ---------
<S>                                                                    <C>             <C>
ASSETS:                                                                                   
                                                                                          
Real Estate:                                                                              
       Land                                                               $ 158,149        $ 158,149
       Buildings and improvements                                           615,604          611,711
       Tenant improvements                                                   40,187           36,170
       Furniture, fixtures and equipment                                      4,355            4,192
                                                                          ---------        ---------
                                                                            818,295          810,222
       Less: Accumulated depreciation and amortization                      (29,118)         (24,393)
                                                                          ---------        ---------
                                                                            789,177          785,829
                                                                                          
Cash and cash equivalents                                                    37,565           27,517
Restricted cash                                                              14,000            9,369
Accounts receivable                                                           5,254           11,946
Prepaid expenses                                                              8,849              495
Deferred costs, net of accumulated                                                        
  amortization of $2,927 and $2,192, respectively                            28,595           22,521
Accrued rent                                                                 39,393           29,969
                                                                          ---------        ---------
                                                                                          
       Total Assets                                                       $ 922,833        $ 887,646
                                                                          =========        =========
                                                                                          
LIABILITIES AND OWNERS' EQUITY                                                            
                                                                                          
Liabilities:                                                                              
Zero coupon convertible debentures, net of unamortized                                    
   discount of $165,214 and $177,696, respectively                        $ 420,971        $ 408,489
14% debentures (includes premium of $24,333 and $24,710, respectively)       99,333           99,710
NationsBank Loans                                                            75,000           55,000
Accrued interest payable                                                      2,720            7,152
Accounts payable and accrued expenses                                        19,684           21,227
Tenant security deposits payable                                             13,523            8,940
                                                                          ---------        ---------
                                                                                          
       Total Liabilities                                                    631,230          600,518
                                                                                          
Commitments and Contingencies                                                             
                                                                                          
Owners' Equity                                                              291,603          287,128
                                                                          ---------        ---------
                                                                                          
       Total Liabilities and Owners' Equity                               $ 922,833        $ 887,646
                                                                          =========        =========
</TABLE>

                      SEE NOTES TO THE FINANCIAL STATEMENTS


                                        1
<PAGE>   4
                                   RCPI TRUST
                           (A Delaware business trust)
                            STATEMENTS OF OPERATIONS
                 FOR THE QUARTERS ENDED MARCH 31, 1998 AND 1997
                                ($ in thousands)
                                   (UNAUDITED)



<TABLE>
<CAPTION>
                                                         March 31, 1998   March 31, 1997
                                                            -------          -------
<S>                                                      <C>              <C>
Revenues:                                                                   
    Base rental                                             $47,461          $43,066
    Operating escalations and percentage rents                1,915            2,774
    Interest and other income                                 1,465            1,810
                                                            -------          -------
        Total revenues                                       50,841           47,650
                                                            -------          -------
Expenses:                                                                   
    Interest                                                 15,423           13,606
    Real estate taxes                                         8,415            8,234
    Payroll and benefits                                      4,391            4,421
    Repairs, maintenance and supplies                         2,838            1,865
    Utilities                                                 3,872            4,453
    Cleaning                                                  3,375            3,640
    Professional fees                                           545            2,725
    Insurance                                                   314              289
    Management and accounting fees                              902              854
    General and administration                                  826              374
    Depreciation and amortization                             5,465            4,523
                                                            -------          -------
        Total expenses                                       46,366           44,984
                                                            -------          -------
Net income                                                  $ 4,475          $ 2,666
                                                            =======          =======
</TABLE>

                      SEE NOTES TO THE FINANCIAL STATEMENTS


                                        2
<PAGE>   5
                                   RCPI TRUST
                           (A Delaware business trust)
                            STATEMENTS OF CASH FLOWS
                 FOR THE QUARTERS ENDED MARCH 31, 1998 AND 1997
                                ($ in thousands)
                                   (UNAUDITED)



<TABLE>
<CAPTION>
                                                                       March 31, 1998   March 31, 1997
                                                                          --------        --------
<S>                                                                    <C>              <C>
Cash Flows from Operating Activities:                                                    
   Net income                                                             $  4,475        $  2,666
   Adjustment to reconcile net income to net cash                                        
   provided by operating activities                                                      
       Amortization of original issue discount and premium                  12,105          10,722
       Depreciation and amortization                                         5,465           4,523
       (Increase) decrease in restricted cash                               (4,631)          2,354
       Decrease in accounts receivable                                       6,692           6,900
       Increase in prepaid expenses                                         (8,354)         (8,411)
       Increase in accrued rent                                             (9,424)         (4,451)
       Increase (decrease) in accounts payable and accrued expenses          1,824          (5,486)
       Decrease (increase) in accrued interest payable                      (4,432)          1,650
                                                                          --------        --------
       Net cash provided by operating activities                             3,720          10,467
                                                                          --------        --------
Cash Flows from Investing Activities:                                                    
    Additions to building and improvements                                  (3,857)         (1,780)
    Additions to tenant improvements                                        (5,827)         (2,882)
    Additions to furniture, fixtures and equipment                            (163)            (28)
    Additions to deferred costs                                             (3,825)         (6,018)
                                                                          --------        --------
       Net cash used in investing activities                               (13,672)        (10,708)
                                                                          --------        --------
Cash Flows from Financing Activities:                                                    
     Additions to NationsBank loans                                         20,000              --
                                                                          --------        --------
       Net cash provided by financing activities                            20,000              --
                                                                          --------        --------
Increase (decrease) in cash and cash equivalents                            10,048            (241)
Cash and cash equivalents at beginning of period                            27,517          28,765
                                                                          --------        --------
Cash and cash equivalents at end of period                                $ 37,565        $ 28,524
                                                                          ========        ========
</TABLE>

                      SEE NOTES TO THE FINANCIAL STATEMENTS


                                        3
<PAGE>   6
                                   RCPI TRUST
                          NOTES TO FINANCIAL STATEMENTS
                                   (UNAUDITED)


1.   FINANCIAL STATEMENTS

     The balance sheet as of March 31, 1998 and the statements of operations and
     cash flows for the three months ended March 31, 1998 and 1997 are
     unaudited, but in the opinion of the Company's management reflect all
     adjustments, consisting only of normal recurring adjustments, which are
     necessary to present fairly the financial condition and results of
     operations at those dates and for those periods. The results of operations
     for the interim periods are not necessarily indicative of results for a
     full year. It is suggested that these financial statements be read in
     conjunction with the audited financial statements and notes thereto
     included in the Company's latest Form 10-K dated December 31, 1997.


2.   DEBT

     NationsBank Credit Facility

     The Company entered into a Credit Agreement (the "NationsBank Credit
     Agreement") dated as of May 16, 1997, with NationsBank of Texas, N.A.
     ("NationsBank"), pursuant to which NationsBank agreed to make term loans
     (the "NationsBank Loans") to the Company in an aggregate principal amount
     of up to $100 million. As of December 31, 1997, the Company had a term loan
     outstanding in the principal amount of $55 million. On January 16, 1998,
     the Company entered into a second NationsBank loan in the principal amount
     of $20 million bringing the aggregate loans due to NationsBank to $75
     million.

3.   SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

     Prior Year Reclassifications

     Certain prior year balances have been reclassified to conform with the
     current year financial statement presentation.


                                        4
<PAGE>   7
                                   RCPI TRUST
                 ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS


     LIQUIDITY AND CAPITAL RESOURCES - RCPI TRUST

     Land and Building

     At March 31, 1998, the Property, exclusive of 1.5 million square feet owned
     directly by the National Broadcasting Company, Inc. and NBC Trust No.
     1996A, was approximately 88.1% occupied. Occupancy rates for the Property
     at various dates are presented in the following table:

       December 31, 1997          86.7%       March 31, 1997           83.3%
       September 30, 1997         86.3%       December 31, 1996        83.6%
       June 30, 1997              86.4%       September 30, 1996       82.8%

     The following table shows selected lease expirations and vacancy of the
     Property as of March 31, 1998. Area, as presented below and discussed
     above, is measured based on standards promulgated by the New York Real
     Estate Board in 1987. Lease turnover could offer an opportunity to increase
     the revenue of the Property or might have a negative impact on the
     Property's revenue. Actual renewal and rental income will be affected
     significantly by market conditions at the time and by the terms at which
     the Company can then lease space.

<TABLE>
<CAPTION>
                              Square Feet               Percent
               Year            Expiring                Expiring
               ----            --------                --------
<S>                           <C>                      <C>  
               Vacant           706,376                  11.9%
               1998             317,324                   5.4%
               1999             192,310                   3.3%
               2000             471,219                   7.9%
               2001             122,638                   2.1%
               2002             210,091                   3.6%
               Thereafter     3,879,739                  65.8%
                              ---------                  -----
               Total          5,899,697                 100.0%
                              =========                 ======
</TABLE>

     Debt

     The Zero Coupons due December 31, 2000 accrete to a face value of
     approximately $586.2 million at an effective annual interest rate of
     12.10%. At March 31, 1998 and December 31, 1997, the carrying value of the
     Debentures, net of unamortized discount, was approximately $420.9 million
     and $408.5 million, respectively.

     The Floating Rate Notes matured on May 31, 1997 and bore interest at the
     London Interbank Offered Rate ("LIBOR") plus 4%. Interest is paid quarterly
     on March 1, June 1, September 1, and December 1. At March 31, 1997 interest
     was accruing at 9.50%. On July 17, 1996, outstanding principal in the
     amount of $106.3 million plus accrued interest of $1.2 million was prepaid.
     On May 16, 1997 the remaining principal balance of $10 million was repaid.

     The 14% Debentures have a principal balance of $75 million and mature on
     December 31, 2007. At the time the Property was acquired by the Company,
     the carrying value of the 14% Debentures was adjusted to reflect their
     estimated fair value at that date, resulting in a premium. The effective
     interest rate, which is net of the


                                        5
<PAGE>   8
                                   RCPI TRUST
                 ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS


     amortization of this premium, is approximately 9.03%. Interest payments are
     made semi-annually on July 31 and January 31. As of March 31, 1998 and
     December 31, 1997, the carrying value of the 14% Debentures was
     approximately $99.3 million and $99.7 million, respectively.

     As of March 31, 1998, the NationsBank credit facility has an aggregate
     principal balance of $75 million and matures on May 16, 2000. The Company
     may elect interest periods based on one, two, three or six month LIBOR
     rates. Interest accrues at LIBOR plus 1.75% and is payable monthly in
     arrears.

     Cash Flow

     During the quarter ended March 31, 1998, the Company received cash flows of
     approximately $3.7 million from operations of the Property. The Company
     used this cash flow from operations to fund in part tenant improvements and
     other leasing costs. The remaining tenant improvement costs, which totaled
     $5.8 million, deferred costs, which totaled $3.8 million, and building and
     improvements of $3.9 million were funded through an additional draw on the
     NationsBank credit facility of $20 million.

     The Company believes that its current cash balance and future cash flows
     from operations, together with its expected borrowings in an amount
     currently believed not to exceed $100 million, will be sufficient to fund
     its requirements for the foreseeable future.

     Inflation

     Inflation and changing prices during the current period did not
     significantly affect the markets in which the Company conducts its
     business. In view of the moderate rate of inflation, its impact on the
     Company's business has not been significant.

     RESULTS OF OPERATIONS - RCPI TRUST

     Base rent for the quarter ended March 31, 1998 increased approximately $4.4
     million from the quarter ended March 31, 1997 partially due to higher
     rental rates on new leases than existed in the prior year. Additionally,
     the occupancy level increased to 88.1% as of March 31, 1998 as compared to
     83.3% as of March 31, 1997.

     Operating escalations have decreased due to a general reduction in overall
     operating expenses from 1996 to 1997. The effect of this reduction was not
     recognized until the second quarter of 1997. As such, operating escalations
     during the first quarter of 1997 are higher than the same period in 1998.

     Interest expense has increased by approximately $1.8 million for the
     quarter ended March 31, 1998 as compared to the quarter ended March 31,
     1997 primarily due to the increase in the outstanding debt balance. Total
     outstanding debt as of March 31, 1997 was approximately $484 million as
     compared to $595 million as of March 31, 1998. The increase is due
     primarily to accretion of the Zero Coupon Debentures and the new



                                        6
<PAGE>   9
                                   RCPI TRUST
                 ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS


     NationsBank credit facility which was not established until May 1997 and
     has increased to $75 million outstanding as of March 31, 1998.

     The increase in repairs and maintenance of approximately $1 million in the
     quarter ended March 31, 1998, as compared to the quarter ended March 31,
     1997, is primarily due to the accelerated timing of certain repairs and
     maintenance projects in 1998.

     Utilities expense has decreased by approximately $582,000 in the first
     quarter of 1998, as compared to the first quarter of 1997, primarily due to
     the unseasonable warm weather in the New York area.

     The decrease in professional fees in 1998 is due primarily to legal and
     professional fees expended during the quarter ended March 31, 1997 in the
     amount of approximately $2 million related to the settlement of the Bear
     Stearns & Co., Inc. and Donaldson, Lufkin & Jenrette Securities Corporation
     lawsuit.

     General and administrative costs have increased in the first quarter of
     1998, as compared to the first quarter of 1997, by approximately $454,000.
     The increase is primarily due to the write off of bad debts in 1998.
     Additionally, there was an increase in certain advertising costs in 1998 to
     promote leasing activity.

     The increase in depreciation and amortization expense of approximately
     $941,000 from the first quarter of 1997 to the first quarter of 1998 is
     primarily due to additional capital expenditures at the property between
     the first quarter of 1997 and the first quarter of 1998. Additionally,
     depreciation has increased due to additional tenant improvements
     expenditures caused by leasing activity.


                                        7
<PAGE>   10
                                   RCPI TRUST
                           PART II - OTHER INFORMATION


     Item 1. Legal Proceedings

     Except as disclosed below, there has been no material change to the status
     of existing litigation as reported in the Company's Form 10-K filed as of
     December 31, 1997.

     On January 21, 1997, an action entitled Flashman v. Goldman, Sachs & Co.,
     97 Civ. 0403 (MGC) (S.D.N.Y.), was filed in New York Federal court
     containing allegations substantially similar to those in the original
     complaint in In re RCPI. Subsequently, the plaintiff in Flashman joined as
     a plaintiff in the amended complaint filed in In re RCPI, and voluntarily
     dismissed the action in Federal Court in New York.

     On February 25, 1997, an action entitled Debora v. Rockefeller, et. al., 97
     Civ. 01312 (LLS) ("Debora"), was filed in the United States District Court
     for the Southern District of New York. The complaint in Debora was
     substantially similar to the original complaint in In re RCPI. The
     defendants are the same in both actions. The Debora complaint alleged
     common law fraud and deceit in addition to the two federal securities law
     violations alleged in In re RCPI. Subsequently, the plaintiff in Debora
     joined as a plaintiff in In re RCPI and voluntarily dismissed the action in
     Federal Court in New York.


                                        8
<PAGE>   11
ITEM 6.  (a) EXHIBITS

         (3.1)    Certificate of Trust of RCPI Trust, dated March 22, 1996 is
                  incorporated by reference to Exhibit 3.1 to the Company's
                  Quarterly Report on Form 10-Q for the fiscal quarter ended
                  June 30, 1996.

         (4.1)    Amended and Restated Debenture Purchase Agreement dated as of
                  July 17, 1996 between the Company and WHRC Real Estate Limited
                  Partnership is incorporated by reference to exhibit 4.1 to the
                  Company's Annual Report on Form 10-K for the year ended
                  December 31, 1996 (the "1996 10-K").

         (4.2)    Indenture dated as of September 15, 1985 between the
                  Predecessor and Manufacturers Hanover Trust Company, as
                  Trustee, including the forms of Current Coupon Convertible
                  Debenture, Zero Coupon Convertible Debenture and Floating Rate
                  Note, is incorporated by reference to Exhibit 4 to the
                  Predecessor's Quarterly Report on Form 10-Q for the period
                  ended September 30, 1985.

         (4.3)    First Supplemental Indenture dated as of December 15, 1985
                  between the Predecessor and the Trustee, is incorporated by
                  reference to the Predecessor's Annual Report on Form 10-K for
                  the year ended December 31, 1985.

         (4.4)    Second Supplemental Indenture dated as of July 10, 1996
                  between the Company and the United States Trust Company of New
                  York, as Trustee is incorporated by reference to exhibit 4.4
                  to the 1996 10-K.

         (4.5)    Instrument of Resignation, Appointment and Acceptance dated as
                  of December 1, 1993 among the Predecessor, Chemical Bank,
                  successor by merger to Manufacturers Hanover Trust Company,
                  and United States Trust Company of New York is incorporated by
                  reference to Exhibit 4.21 to the Predecessor's Annual Report
                  on Form 10-K for the year ended December 31, 1993.

         (10.1)   Amended and Restated Loan Agreement dated as of July 17, 1996
                  among the Company, the lenders parties thereto and GSMC, as
                  agent, is incorporated by reference to Exhibit 10.1 to the
                  1996 10-K.

         (10.2)   Guarantee dated July 17, 1996 by Whitehall Street Real Estate
                  Limited Partnership V, Exor Group S.A., Tishman Speyer Crown
                  Equities, David Rockefeller, Troutlet Investments Corporation,
                  Gribble Investments (Tortola) BVI, Inc. and Weevil Investments
                  (Tortola) BVI, Inc., as guarantors in favor of GSMC, as agent
                  and lender, is incorporated by reference to Exhibit 10.2 to
                  the 1996 10-K.

         (10.3)   Agreement and Plan of Merger dated as of November 7, 1995
                  among the Predecessor, RCPI Holdings Inc., RCPI Merger Inc.,
                  Whitehall Street Real Estate Limited Partnership V, Rockprop,
                  L.L.C., David Rockefeller, Exor Group S.A. and Troutlet
                  Investments Corporation is incorporated by reference to
                  Exhibit 10.28 to the Predecessor's Current Report on Form 8-K
                  dated November 13, 1995.

         (10.4)   Amendment No. 1 dated as of February 12, 1996 to the Agreement
                  and Plan of Merger dated as of November 7, 1995 among the
                  Predecessor, RCPI Holdings Inc., RCPI Merger Inc.,


                                        9
<PAGE>   12
ITEM 6.  (a) EXHIBITS (Cont'd)

                  Whitehall Street Real Estate Limited Partnership V, Rockprop,
                  L.L.C., David Rockefeller, Exor Group S.A. and Troutlet
                  Investments Corporation is incorporated by reference to
                  Exhibit 10.31 to the Predecessor's Current Report on Form 8-K
                  dated February 22, 1996.

         (10.5)   Amendment No. 2 to the Agreement and Plan of Merger, dated as
                  of April 25, 1996 is incorporated herein by reference to the
                  Predecessor's Current Report on Form 8-K, filed on April 25,
                  1996.

         (10.6)   Amendment No. 3 to the Agreement and Plan of Merger, dated as
                  of May 29, 1996 is incorporated herein by reference to the
                  Predecessor's Current Report on Form 8-K, filed on May 29,
                  1996.

         (10.7)   Amendment No. 4 to the Agreement and Plan of Merger, dated as
                  of June 30, 1996 is incorporated herein by reference to the
                  Predecessor's Current Report on Form 8-K, filed on July 1,
                  1996.

         (10.8)   Credit Agreement, dated as of May 16, 1997, between the
                  Company and NationsBank of Texas, N.A. is incorporated by
                  reference to Exhibit 4.6 to the Company's Quarterly Report on
                  Form 10- Q for the period ended June 30, 1997.

         (10.9)   Intercreditor and Subordination Agreement, dated as of May 16,
                  1997, between the Company and Whitehall is incorporated by
                  reference to Exhibit 4.7 to the Company's Quarterly Report on
                  Form 10-Q for the period ended June 30, 1997.

         (10.10)  Limited Resource Agreement, dated as of May 16, 1997, is 
                  incorporated by reference to Exhibit 4.8 to the Company's 
                  Quarterly Report on Form 10-Q for the period ended June 30, 
                  1997.

         (27.1)   Company's Financial Data Schedule.


      (b) REPORTS ON FORM 8-K

         No Current Reports on Form 8-K have been filed during the last fiscal
quarter.


                                       10
<PAGE>   13
                                   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.


                                       RCPI TRUST




Date: May 15, 1998                     By: /s/ David Augarten
                                         -----------------------
                                           David Augarten
                                           Vice President
                                           (Principal Financial Officer)


                                       11