<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D. C. 20549

                                    Form 10-Q

(Mark One)

 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 0-5641

                           CLEVETRUST REALTY INVESTORS
             (Exact name of registrant as specified in its charter)

             Massachusetts                              34-1085584
(State or other jurisdiction of           (I. R. S. Employer Identification No.)
incorporation or organization)

2001 Crocker Road, Suite 400
        Westlake, Ohio                                    44145
(Address of Principal Executive Offices)               (Zip Code)
                                  (440) 899-0909

              (Registrant's telephone number, including area code)

                                 Not Applicable
 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 ________

Shares of Beneficial Interest Outstanding at May 11, 1998:  5,136,616



<PAGE>   2


                           CLEVETRUST REALTY INVESTORS

                                      INDEX


<TABLE>
<CAPTION>

                                                                                   Page


<S>                                                                                 <C>
PART I.  FINANCIAL INFORMATION:

         Item 1.  Financial Statements

                  Statements of Financial Condition
                   -- March 31, 1998 and September 30, 1997                         3

                  Statements of Operations
                   -- Three Months and Six Months ended March 31, 1998 and 1997     4

                  Statements of Cash Flows
                   -- Six Months ended March 31, 1998 and  1997                     5

                  Notes to Financial Statements                                     6


         Item 2.  Management's Discussion and Analysis of Financial Condition
                     and Results of Operations                                      8


PART II. OTHER INFORMATION:

         Item 1.    Legal Proceedings                                              11

         Item 2.    Changes in Securities                                          11

         Item 3.    Defaults upon Senior Securities                                11

         Item 4.    Submission of Matters to a Vote of Security Holders            11

         Item 5.    Other Information                                              11

         Item 6.    Exhibits and Reports on Form 8-K                               11
</TABLE>



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<PAGE>   3


CLEVETRUST REALTY INVESTORS
STATEMENTS OF FINANCIAL CONDITION

<TABLE>
<CAPTION>

                                                                   MARCH 31, 1998              SEPTEMBER 30, 1997
                                                                ----------------------     --------------------------
                                                                                 (in thousands)
<S>                                                                            <C>                           <C>    

ASSETS
-----------------------------------------------------------

Invested assets - NOTE B:
  Properties held for sale                                                     $3,254                        $12,918
  Valuation reserve                                                                77                            260
                                                                ----------------------     --------------------------
                                                                                3,177                         12,658

Cash and cash equivalents                                                       2,207                          4,612
Other assets                                                                       98                            368
                                                                ----------------------     --------------------------

                                              TOTAL ASSETS                     $5,482                        $17,638
                                                                ======================     ==========================


LIABILITIES
-----------------------------------------------------------

Mortgage notes payable - NOTE B                                                    $0                         $5,561
Accrued federal and state income taxes - NOTE A                                   381                          2,085
Accrued expenses and other liabilities - NOTE C                                   914                          3,184
                                                                ----------------------     --------------------------

                                         TOTAL LIABILITIES                      1,295                         10,830

SHAREHOLDERS' EQUITY
-----------------------------------------------------------

Shares of Beneficial Interest, par value $1 per Share:
    Authorized - - Unlimited
    Issued and outstanding shares - 5,136,616                                   5,137                          5,137
Additional paid-in capital                                                      5,816                          9,412
Accumulated deficit                                                            (6,766)                        (7,741)
                                                                ----------------------     --------------------------
                                TOTAL SHAREHOLDERS' EQUITY                      4,187                          6,808
                                                                ----------------------     --------------------------

                TOTAL LIABILITIES AND SHAREHOLDERS' EQUITY                     $5,482                        $17,638
                                                                ======================     ==========================

</TABLE>

See notes to financial statements.




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<PAGE>   4


CLEVETRUST REALTY INVESTORS
STATEMENTS OF OPERATIONS

The following statements of operations of CleveTrust Realty Investors for the
three-month and six-month periods ended March 31, 1998 and 1997, respectively,
are unaudited, but in the opinion of management include all adjustments
necessary to present fairly the results of operations. All such adjustments were
of a normal recurring nature. The results of operations for the three-month and
six-month periods ended March 31, 1998 are not necessarily indicative of the
results of operations for succeeding periods.

<TABLE>
<CAPTION>

                                                                             Three Months Ended            Six Months Ended
                                                                        --------------------------     --------------------------
                                                                        3/31/98         3/31/97        3/31/98         3/31/97
                                                                        -----------     ----------     -----------     ----------
                                                                                  (in thousands, except per share data)

<S>                                                                           <C>          <C>               <C>          <C>   
INCOME

Real estate operations:
  Rental Income                                                               $273         $2,278            $942         $4,770

  Less:  Real estate operating expenses                                         53          1,094             297          2,200
                                                                        -----------     ----------     -----------     ----------
Income from real estate operations                                             220          1,184             645          2,570
Interest income                                                                 29             43              82             63
Other                                                                           38             91              68             93
                                                                        -----------     ----------     -----------     ----------
                                                                               287          1,318             795          2,726

EXPENSES

Interest:
  Mortgage notes payable                                                        36            178             151            362
  Bank notes payable                                                             0            126               0            294
                                                                        -----------     ----------     -----------     ----------
                                                                                36            304             151            656
General and administrative                                                     166            632             376          1,168
Provision for valuation reserve - NOTE B                                         0              0             (54)             0
                                                                        -----------     ----------     -----------     ----------
                                                                               202            936             473          1,824
                                                                        -----------     ----------     -----------     ----------
Income before gains on sales of real estate and
  income taxes                                                                  85            382             322            902
Gains on sales of real estate - NOTE B                                         743          6,594           1,116          7,170
Federal and state income taxes - NOTE A                                       (255)             0            (463)             0
                                                                        -----------     ----------     -----------     ----------

                                                        NET INCOME            $573         $6,976            $975         $8,072
                                                                        ===========     ==========     ===========     ==========

Per Share of Beneficial Interest - NOTE E:
   Income before gains on sales of real estate and
     income taxes                                                            $0.02          $0.07           $0.06          $0.18
  Gains on sales of real estate                                               0.14           1.28            0.22           1.39
  Federal and state income taxes                                             (0.05)          0.00           (0.09)          0.00
                                                                        -----------     ----------     -----------     ----------
                                             NET INCOME  PER SHARE           $0.11          $1.36           $0.19          $1.57
                                                                        ===========     ==========     ===========     ==========

Weighted Average Number of Shares of
  Beneficial Interest Outstanding                                            5,137          5,137           5,137          5,140
                                                                        ===========     ==========     ===========     ==========
</TABLE>

See notes to financial statements.




                                      -4-
<PAGE>   5


CLEVETRUST REALTY INVESTORS
STATEMENTS OF CASH FLOWS

<TABLE>
<CAPTION>

                                                                                  Six Months Ended
                                                                            -----------------------------
                                                                              3/31/98          3/31/97
                                                                            ------------     ------------
                                                                                    (in thousands)

<S>                                                                              <C>                   <C>
CASH FLOW FROM OPERATING ACTIVITIES:
Net income                                                                         $975           $8,072
Non-cash revenues and expenses included in income:
  Decrease in other assets                                                          270            2,361
  Decrease in accrued interest on notes payable                                       0              (14)
  Decrease in accrued federal and state income taxes                             (1,704)               0
  Decrease in accrued expenses and other liabilities                             (2,270)            (329)
Reconciliation to net cash flow from operating activities:
  Gain on sales of real estate                                                   (1,116)          (7,170)
                                                                            ------------     ------------
                         Cash Flow (Used In) From Operating Activities           (3,845)           2,920

CASH FLOW FROM INVESTING ACTIVITIES:
Equity investments:
  Improvements to existing properties                                                 0             (517)
  Proceeds from properties sold                                                  10,597           16,945
Real estate mortgage loan repayments                                                  0               37
                                                                            ------------     ------------
                                   Cash Flow From Investing Activities           10,597           16,465

CASH FLOW FROM FINANCING ACTIVITIES:
Mortgage notes payable:
  Principal amortization payments                                                   (47)            (110)
  Principal repayments                                                           (5,514)          (1,208)
Bank notes payable:
  Repayments                                                                          0           (9,800)
Shares repurchased and subsequently retired                                           0             (202)
Distributions to shareholders                                                    (3,596)               0
                                                                            ------------     ------------
                              Cash Flow (Used In) Financing Activities           (9,157)         (11,320)
                                                                            ------------     ------------

(Decrease) increase in cash and short-term investments                           (2,405)           8,065
Balance at beginning of year                                                      4,612            1,490
                                                                            ------------     ------------

Balance at end of period                                                         $2,207           $9,555
                                                                            ============     ============
</TABLE>

See notes to financial statements.



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<PAGE>   6


                           CLEVETRUST REALTY INVESTORS
                          NOTES TO FINANCIAL STATEMENTS
                                 March 31, 1998


NOTE A - INCOME TAXES

For the six month period ended March 31, 1998 the Trust recorded federal income
taxes of $502,000 ($641,000 of current taxes, net of a deferred tax asset of
$139,000). Additionally, the Trust recorded state tax refunds of $39,000 during
this period. The Trust had no income tax expense for the six month period ended
March 31, 1997. For the fiscal year ended September 30, 1997 the Trust recorded
federal income taxes of $2,400,000 ($2,531,000 of current taxes, net of a
deferred tax asset of $131,000) and state income taxes of $314,000.

On April 13, 1998 the Trust filed its federal income tax return for the tax year
ended September 30, 1997, which showed that the Trust owed and paid taxes of
$2,474,250 for the year.

The Trust had a net deferred tax asset position at March 31, 1998 of
approximately $270,000. At September 30, 1997 the Trust had a net deferred tax
asset position of approximately $131,000.

NOTE B - INVESTED ASSETS

On December 8, 1997 the Trust completed a $3,150,000 sale of the Petroleum Club
Building located in Tulsa, Oklahoma. This sale resulted in a gain of
approximately $373,000. On December 15, 1997 the Trust completed a $643,000 sale
of a vacant restaurant located in Davenport, Iowa. This sale resulted in a loss
of approximately $129,000 which had previously been provided for in the
Valuation Reserve. The Valuation Reserve on this property was $183,000, after
applying the loss of $129,000 the balance of $54,000 was reversed. On January
30, 1998 the Trust completed a $7,400,000 sale of the Cannon West Shopping
Center located in Austin, Texas. This sale resulted in a gain of approximately
$743,000. In connection with this sale, the Trust repaid in full the $5,514,000
first mortgage loan which was secured by the Cannon West Shopping Center.

NOTE C - ACCRUED EXPENSES AND OTHER LIABILITIES

At September 30, 1997 the Trust had accrued $1,160,000 of severance payments due
the officers and employees of the Trust in connection with the Plan for the
Orderly Liquidation of the Trust (the "Plan"). These payments were to be made at
the termination of the individuals' employment upon receipt by the Trust of a
release of all claims against the Trust. On October 24, 1997 the Trustees
prepaid the severance payments after obtaining the required releases. By
prepaying the severance, the payments were shown as an expense on the Trust's
1997 tax return. Additionally, at September 30, 1997 the Trust had accrued
$1,540,000 for certain other payments to be paid to the officers based on the
Trust's ability to achieve defined distributions to shareholders. Based on the
liquidating distribution of $.70 per share paid on January 19, 1998 the Trust
made payments to the officers of approximately $772,000.








                                      -6-
<PAGE>   7

                           CLEVETRUST REALTY INVESTORS
                   NOTES TO FINANCIAL STATEMENTS - (Continued)


NOTE D - DISTRIBUTIONS

On January 19, 1998 the Trust paid a liquidating distribution of $.70 per share
to shareholders of record as of January 12, 1998. With the payment of this
distribution, the combined per share amount of liquidating distributions paid to
shareholders totals $6.40 since the effective date of the Plan, April 29,1998.

NOTE E - NET INCOME PER SHARE

Net income per Share of Beneficial Interest has been computed using the weighted
average number of Shares of Beneficial Interest outstanding each period. As the
Trust has no options or warrants outstanding, there is no difference between
basic and diluted net income per share.






























                                      -7-
<PAGE>   8


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


FINANCIAL CONDITION

At March 31, 1998 the Trust's invested assets consisted of properties held for
sale, net of a $77,000 valuation reserve, of $3,177,000. This compared with
properties held for sale, net of a $260,000 valuation reserve, of $12,658,000 at
September 30, 1997. The change since year end was due to the December 8, 1997
sale of the Petroleum Club Building, located in Tulsa, Oklahoma, the December
15, 1997 sale of a vacant restaurant, located in Davenport, Iowa, and the
January 30, 1998 sale of the Cannon West Shopping Center, located in Austin,
Texas. The decrease in the Trust's cash and cash equivalents was primarily due
to the January 19, 1998 liquidating distribution of $.70 per share paid to
shareholders of record of January 12, 1998. The $270,000 decline in other assets
was primarily due to the collection of certain receivables which were due from
several tenants for annual rental adjustments and the amortization of certain
prepaid expenses.

In connection with the January 30, 1998 sale of the Cannon West Shopping Center
the Trust repaid the $5,514,000 first mortgage loan which was secured by that
property. At September 30, 1997 the Trust had accrued $1,160,000 of severance
payments due the officers and employees of the Trust in connection with the
Plan. These payments were to be made at the termination of the individuals'
employment upon receipt by the Trust of a release of all claims against the
Trust. On October 24, 1997 the Trustees prepaid the severance payments after
obtaining the required releases. By prepaying the severance, the payments were
shown as an expense on the Trust's 1997 tax return. Additionally, at September
30, 1997 the Trust had accrued $1,540,000 for certain other payments to be paid
to the officers based on the Trust's ability to achieve defined distributions to
shareholders. Based on the liquidating distribution of $.70 per share paid on
January 19, 1998 the Trust made payments to the officers of approximately
$772,000. These two payments were the primary reason for the decrease in accrued
expenses and other liabilities at March 31, 1998 from September 30, 1997.

The $2,621,000 decrease in shareholders' equity at March 31, 1998 from September
30, 1997 was the net effect of the Trust recording net income of $975,000 and
making a liquidating distribution of $3,596,000 on January 19, 1998.

RESULTS OF OPERATIONS

Quarter ended March 31, 1998 versus March 31, 1997:

Income from real estate operations during the quarter ended March 31, 1998
decreased $964,000 (81%) when compared to the quarter ended March 31, 1997.
Rental income for the quarter ended March 31, 1998 decreased $2,005,000 (88%)
compared to the quarter ended March 31, 1997. Real estate operating expenses
decreased $1,041,000 (95%) in the three months ended March 31, 1998 versus 1997.
The declines were primarily the result of the Trust selling eleven properties
during the year ended September 30, 1997 and three more properties during the
current fiscal year. All sales were in accordance with the Plan for the
Liquidation of the Trust.




                                      -8-
<PAGE>   9


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

RESULTS OF OPERATIONS - (Continued)

The $268,000 (88%) decrease in interest expense for the three month period ended
March 31, 1998 when compared to the same period one year ago was primarily due
to the Trust's repayment of a $5,514,000 first mortgage loan in January, 1998,
as described above, and the repayment in full of the $9,800,000 revolving line
of credit ("1994 Credit") issued by National City Bank of Cleveland and
Manufacturer's and Traders Trust Company of Buffalo, New York. General and
Administrative expenses decreased $466,000 (74%) in the quarter ended March 31,
1998 compared to the quarter ended March 31, 1997 primarily because certain
expenses incurred in the 1997 period ($266,000 in severance payable to officers
and employees and $72,000 related to the Plan) did not recur in the 1998 period.

As previously mentioned, the Trust completed the $7,400,000 sale of the Cannon
West Shopping Center, located in Austin, Texas on January 30, 1998. This sale
resulted in a gain of approximately $743,000. During the three months ended
March 31, 1997 the Trust completed three sales, all of which resulted in gains.
The first was the January 21, 1997 $5,950,000 sale of the Warren Plaza Shopping
Center located in Dubuque, Iowa. This sale resulted in a gain of approximately
$1,727,000. The second was the February 28, 1997 $3,475,000 sale of the Triangle
Square Retail Center located in Hilton Head, South Carolina. This sale resulted
in a gain of $2,550,000. The third was the March 12, 1997 $5,350,000 sale of the
Englewood Bank Building located in Englewood, Colorado. This sale resulted in a
gain of approximately $2,317,000.

During the quarter ended March 31, 1998 the Trust recorded federal income tax
expense of $296,000 ($628,000 of current taxes, net of a deferred tax asset of
$332,000). Additionally, the Trust recorded state tax refunds of $39,000 during
this period. There was no income tax expense for the quarter ended March 31,
1997.

Six Months ended March 31, 1998 versus March 31, 1997:

Income from real estate operations in the six months ended March 31, 1998
decreased $1,925,000 (75%) compared to the six months ended March 31, 1997.
Rental income for the six months ended March 31, 1998 decreased $3,828,000 (80%)
when compared to the six months ended March 31, 1997. Real estate operating
expenses during the current six months decreased $1,903,000 (87%) when compared
to the same period one year ago. The declines were primarily due to the sales of
properties, as described above.

The $505,000 (77%) decrease in interest expense for the six month period ended
March 31, 1998 when compared to the same period one year ago was primarily due
to the repayment of the $5,514,000 first mortgage and the $9,800,000 of
borrowings under the 1994 Credit. Both of these repayments were previously
discussed. General and administrative expenses decreased $792,000 (68%) in the
six months ended March 31, 1998 compared to the six months ended March 31, 1997
primarily because certain expense incurred in the 1997 period ($533,000 in
severance payable to officers and employees and $147,000 related to the Plan)
did not recur in the 1998 period. Also, during the six months ended March 31,
1998 the Trust reversed $54,000 of valuation reserve which was related to the
sale of a vacant restaurant, as the loss on the sale was less than anticipated
at the time the reserve was established.



                                      -9-
<PAGE>   10


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

RESULTS OF OPERATIONS - (continued)

In addition to the gains for both quarters ended March 31, 1998 and 1997
discussed previously, the six month period ended March 31, 1998 includes the
$373,000 gain on the December 8, 1997 sale of the Petroleum Club Building
located in Tulsa, Oklahoma. The six month period ended March 31, 1997 also
includes the $563,000 gain on the October 7, 1996 sale of the Littleton Bank
Building located in Littleton, Colorado and the $13,000 gain on the December 30,
1996 sale of a .23 acre parcel of land located in Dubuque, Iowa.

OUTLOOK

Tiffany Plaza and a 20 acre vacant land parcel are the only remaining properties
of the Trust. Effective May 1, 1998 the Trust executed a contract of sale for
Tiffany Plaza, Ardmore, Oklahoma for a sales price of $3,400,000. The contract
provides for a due diligence period, during which time the buyer could cancel
the contract at its option. Upon completion of the due diligence period the
buyer would either place a non-refundable deposit with the Trust or cancel the
contract. Thereafter, should the buyer fail to complete the sale, the deposit
would be forfeited and retained by the Trust. Therefore, there is no guarantee
that Tiffany Plaza would actually be sold for the price stated. It should be
noted that Tiffany Plaza was previously under a contract of sale which was
executed effective January 28, 1998. This contract was canceled by the buyer
during the due diligence period. Management of the Trust does not believe the
cancellation was the result of factors that will materially affect the ability
of the Trust to sell the Property.

Item 3.  Quantitative and Qualitative Disclosures About Market Risk.

Not applicable.

















                                      -10-
<PAGE>   11


                                     PART II


Item 1.    Legal Proceedings

           There are no items or events requiring reporting with respect to this
           item.

Item 2.    Changes in Securities

           There are no items or events requiring reporting with respect to this
           item.

Item 3.    Defaults upon Senior Securities

           There are no items or events requiring reporting with respect to this
           item.

Item 4.    Submission of Matters to a Vote of Security Holders

           There are no items or events requiring reporting with respect to this
           item.

Item 5.    Other Information

           None

Item 6.    Exhibits and Reports on Form 8-K

           (a)  Exhibits

                Exhibit (27):  Financial Data Schedule

           (b)  Form 8-K dated January 31, 1998

                Item 5. Other Events - - On February 26, 1998 CleveTrust Realty
                Investors (the "Trust") was informed by The Nasdaq Stock Market,
                Inc. ("Nasdaq") that the Trust was not in compliance with the
                net tangible assets requirement under Maintenance Standard 1,
                pursuant to NASD Marketplace Rule 4450(a)(3), which became
                effective on February 23, 1998. The rule calls for a minimum net
                asset value of $4,000,000. On March 5,1998 the Trust responded
                to Nasdaq that as of January 31, 1998 the Trust did have a net
                asset value in excess of $4,000,000 as a result of the January
                30, 1998 sale of one of the Trust's properties. The Trust
                supplied Nasdaq with a copy of its January, 1998 internal
                statements as support. On March 13, 1998 Nasdaq responded to the
                Trust that the supporting statements needed to be public
                statements. Therefore, the Trust filed, as Exhibit 99.1 to Form
                8-K, a copy of its unaudited financial statements and related
                footnotes for the month ended January 31, 1998.






                                      -11-
<PAGE>   12


                                   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.






                                       CLEVETRUST REALTY INVESTORS
                                              (Registrant)







Date:    May 11, 1998                By: /s/ John C. Kikol
                                        ------------------------------
                                             John C. Kikol, President







Date:    May 11, 1998                By: /s/ Michael R. Thoms
                                        ------------------------------
                                             Michael R. Thoms, Vice President
                                                 and Treasurer


                                      -12-
<PAGE>   13


                           CLEVETRUST REALTY INVESTORS

         QUARTERLY REPORT ON FORM 10-Q FOR QUARTER ENDED MARCH 31, 1997

                                  EXHIBIT INDEX



 
Exhibit No.                                     Description
-----------                                     -----------

   (27)                                    Financial Data Schedule.

 




















                                     - 13 -