COLONIAL INTERMEDIATE HIGH INCOME FUND
DEF 14A, 1998-03-20
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                     COLONIAL INTERMEDIATE HIGH INCOME FUND
                One Financial Center, Boston, Massachusetts 02111
                                 (617) 426-3750


                    NOTICE OF ANNUAL MEETING OF SHAREHOLDERS
                            TO BE HELD APRIL 29, 1998



Dear Shareholder:

         The Annual Meeting of Shareholders (Meeting) of Colonial Intermediate
High Income Fund (Fund) will be held at the offices of Colonial Management
Associates, Inc. (Adviser), One Financial Center, Boston, Massachusetts, on
Wednesday, April 29, 1998, at 10:00 a.m. Eastern time, to:

           1.  Elect five Trustees;

           2.  Ratify the selection of independent accountants; and 

           3.  Transact such other business as may properly come before the
               Meeting or any adjournment thereof.

                                            By order of the Trustees,



                                            Michael H. Koonce, Secretary

March 20, 1998


NOTICE: YOUR VOTE IS IMPORTANT, REGARDLESS OF THE NUMBER OF SHARES YOU OWN. IF A
QUORUM IS NOT PRESENT AT THE MEETING, ADDITIONAL EXPENSES WILL BE INCURRED TO
SOLICIT ADDITIONAL PROXIES. TO AVOID THESE COSTS TO YOUR FUND, PLEASE VOTE, SIGN
AND RETURN YOUR PROXY IN THE ENCLOSED POSTAGE-PAID ENVELOPE IMMEDIATELY.

IH-85/889E-0298



<PAGE>


                                 PROXY STATEMENT
                               General Information

                                                                  March 20, 1998

         The enclosed proxy, which was first mailed on March 20, 1998, is
solicited by the Trustees for use at the Meeting. All properly executed proxies
received in time for the Meeting will be voted as specified in the proxy or, if
no specification is made, in favor of each proposal referred to in the Proxy
Statement. The proxy may be revoked prior to its exercise by a later dated
proxy, by written revocation received by the Secretary or by voting in person.
Solicitation may be made by mail, telephone, telegraph, telecopy and personal
interviews. Authorization to execute proxies may be obtained by telephonically
or electronically transmitted instructions. The cost of solicitation will be
paid by the Fund.

         Holders of a majority of the shares outstanding and entitled to vote
constitute a quorum and must be present in person or represented by proxy for
business to be transacted at the Meeting. On February 2, 1998, the Fund had
outstanding 14,897,108.541 shares of beneficial interest. Shareholders of record
at the close of business on February 2, 1998 will have one vote for each share
held. As of February 2, 1998, The Depository Trust Company (Cede & Co.), 7
Hanover Square, New York, New York 10004, owned of record 12,893,683 shares
representing 86.55% of the Fund's outstanding shares.

         Votes cast by proxy or in person will be counted by persons appointed
by the Fund to act as election tellers for the Meeting. The tellers will count
the total number of votes cast "for" approval of the proposals for purposes of
determining whether sufficient affirmative votes have been cast. Where a
shareholder withholds authority or abstains, or the proxy reflects a "broker
non-vote" (i.e., shares held by brokers or nominees as to which (i) instructions
have not been received from the beneficial owners or persons entitled to vote
and (ii) the broker or nominee does not have discretionary voting power on a
particular matter), the shares will be counted as present and entitled to vote
for purposes of determining the presence of a quorum. With respect to the
election of Trustees and ratification of independent accountants, withheld
authority, abstentions and broker non-votes have no effect on the outcome of the
voting.

         Further information concerning the Fund is contained in its most recent
Annual Report to shareholders, which is obtainable free of charge by writing the
Adviser at One Financial Center, Boston, MA 02111 or by calling 1-800-426-3750.

                                       2

<PAGE>


1.    Election of Five Trustees.

      Messrs. Birnbaum, Grinnell, Lowry, Mayer and Sullivan (who have each
agreed to serve) are proposed for election as Trustees of the Fund, each to
serve for three years, with the exception of Mr. Grinnell who will serve for two
years, or until a successor is elected. The Board of Trustees currently consists
of Ms. Collins and Messrs. Birnbaum, Bleasdale, Grinnell, Ireland, Lowry, Mayer,
Moody, Neuhauser, Shinn, Sullivan and Weeks. Effective April 24, 1998, Messrs.
Ireland, Shinn and Weeks will retire as Trustees of the Fund.

      The Board of Trustees is divided into the following three classes, each
with a three year term expiring in the years indicated (assuming the persons
listed above are elected at the Meeting):

        1999                     2000                     2001
        ----                     ----                     ----

        Mr. Bleasdale            Mr. Grinnell             Mr. Birnbaum
        Ms. Collins              Mr. Moody                Mr. Lowry
        Mr. Neuhauser                                     Mr. Mayer
                                                          Mr. Sullivan


      The following table sets forth certain information about the Board of
Trustees:

<TABLE>
<CAPTION>
                                                                          Shares
                                                                       Beneficially
                                                                        Owned and
                                                                         Percent
                                                                        of Fund at
Name         Trustee                                                   February 2,
(Age)        Since      Principal Occupation(1) and Directorships        1998 (2)
<S>                     <C>                                                <C> 
Robert J. Birnbaum      Retired (formerly Special Counsel, Dechert
(70)           1995     Price & Rhoads--law). Director or Trustee:
                        Colonial Funds, Liberty All-Star Equity Fund,
                        Liberty All-Star Growth Fund, Inc., The            
                        Emerging Germany Fund.                             -0-

Tom Bleasdale           Retired (formerly Chairman of the Board and
(67)           1988     Chief Executive Officer, Shore Bank & Trust
                        Company--banking). Director or Trustee:
                        Colonial Funds, Empire Company Limited.            -0-

Lora S. Collins         Attorney (formerly Attorney, Kramer, Levin,
(62)           1988     Naftalis & Frankel--law).  Trustee:  Colonial      
                        Funds.                                             -0-

                                       3

<PAGE>

James E. Grinnell       Private Investor.  Director or Trustee:
(68)           1995     Colonial Funds, Liberty All-Star Equity Fund,
                        Liberty All-Star Growth Fund, Inc.                 -0-

Richard W. Lowry        Private Investor.  Director or Trustee:
(61)           1995     Colonial Funds, Liberty All-Star Equity Fund,
                        Liberty All-Star Growth Fund, Inc.                 -0-

William E. Mayer*       Partner, Development Capital, LLC
(57)           1994     (investments)  (formerly Dean of the College
                        of Business and Management, University of
                        Maryland--higher education; Dean of the Simon
                        Graduate School of Business, University of
                        Rochester--higher education).  Director or
                        Trustee: Colonial Funds, Hambrecht & Quist
                        Incorporated, Chart House Enterprises, Johns       
                        Manville.                                          -0-

James L. Moody, Jr.     Retired (formerly Chairman of the Board,
(66)           1988     Chief Executive Officer and Director,
                        Hannaford Bros. Co.-food distributor).
                        Director or Trustee: Colonial Funds,
                        Penobscot Shoe Co., Staples, Inc., UNUM
                        Corporation, IDEXX Laboratories, Inc., Empire      
                        Company Limited.                                   -0-

John J. Neuhauser       Dean of the School of Management, Boston
(55)           1992     College (higher education). Director or
                        Trustee: Colonial Funds, Hyde Athletic             
                        Industries, Inc.                                   -0-

Robert L. Sullivan      Retired Partner, Peat Marwick Main & Co.
(70)           1989     (management consulting) (formerly
                        self-employed Management Consultant).              
                        Trustee: Colonial Funds.                           -0-
</TABLE>

*        Mr. Mayer is an "interested person," as defined in the Investment
         Company Act of 1940 (1940 Act), because of his affiliation with
         Hambrecht & Quist Incorporated (a registered broker-dealer).
(1)      Except as otherwise noted, each individual has held the office
         indicated or other offices in the same company for the last five years.
(2)      On February 2, 1998, the Trustees and officers of the Fund as a group
         beneficially owned less than 1% of the then outstanding shares of the
         Fund.

         In this Proxy Statement, the "Colonial Funds" means Colonial Trust I,
Colonial Trust II, Colonial Trust III, Colonial Trust IV, Colonial Trust V,
Colonial Trust VI, Colonial Trust VII, LFC Utilities Trust, Colonial High Income
Municipal Trust, Colonial InterMarket Income Trust I, Colonial Intermediate High
Income Fund, Colonial Investment Grade Municipal Trust and Colonial Municipal
Income Trust.

                                       4

<PAGE>

         The following table sets forth certain information about the executive
officers of the Fund:

<TABLE>
<CAPTION>
                                                                            Shares
               Executive                                                    Beneficially
Name           Officer                                                      Owned and
(Age)          Since                                                        Percent of
                                                                            Fund at
                                                                            February 2,
                            Office with Fund; Principal Occupation (3)      1998 (4)

<S>                         <C>                                              <C>
Harold W. Cogger            President of the Fund and of the Colonial
(62)         1993           Funds since March, 1996 (formerly Vice
                            President from July, 1993 to March, 1996);
                            Chairman of the Board since March, 1996 and
                            Director since March, 1984 of the Adviser
                            (formerly President from July, 1993 to
                            December, 1996, Chief Executive Officer from
                            March, 1995 to December, 1996 and Executive
                            Vice President from October, 1989 to July,
                            1993); Director since October, 1991 and
                            Chairman of the Board since March, 1996 of
                            The Colonial Group, Inc. (TCG) (formerly
                            President from October, 1994 to December,
                            1996 and Chief Executive Officer from March,
                            1995 to December, 1996);  Executive Vice
                            President and Director since March, 1995 of
                            Liberty Financial Companies, Inc. (Liberty       
                            Financial). Director or Trustee: Liberty
                            All-Star Equity Fund, Liberty All-Star Growth
                            Fund, Inc., Stein Roe & Farnham Incorporated.    -0-

Davey S. Scoon              Vice President of the Fund and of the
(51)           1993         Colonial Funds since June, 1993 (formerly
                            Treasurer from March, 1985 to June, 1993);
                            Executive Vice President since July, 1993 and
                            Director since March, 1985 of the Adviser
                            (formerly Senior Vice President and Treasurer
                            from March, 1985 to July, 1993); Executive
                            Vice President and Chief Operating Officer
                            since March, 1995 of TCG (formerly Vice
                            President - Finance and Administration and       
                            Treasurer from November, 1985 to March, 1995).   -0-
                          
Carl C. Ericson             Vice President of the Fund since February,
(55)           1989         1989; Senior Vice President, Director and
                            Manager of the Taxable Fixed Income Group since
                            March, 1996 of the Adviser (formerly Vice President
                            from January, 1992 to March, 1996).              -0-
                          

                                       5

<PAGE>


Andrea S. Feingold          Vice President of the Fund since June, 1993;
(34)           1993         Vice President and head of the Corporate
                            Group since November, 1993 of the Adviser (formerly
                            Assistant Treasurer from June, 1991 to June, 1992
                            and Assistant Vice President and Analyst of the
                            Adviser from July, 1992 to June, 1993).          -0-
                          
Timothy J. Jacoby           Treasurer and Chief Financial Officer of the
(45)           1996         Fund and of the Colonial Funds since October,
                            1996 (formerly Controller and Chief
                            Accounting Officer from October, 1997 to
                            February, 1998); Senior Vice President since
                            September, 1996 of the Adviser (formerly
                            Senior Vice President, Fidelity Accounting
                            and Custody Services from September, 1993 to
                            September, 1996 and Assistant Treasurer from     
                            August, 1990 to September, 1993 to the
                            Fidelity Group of Funds).                        -0-

J. Kevin Connaughton        Controller and Chief Accounting Officer of
(33)           1998         the Fund and of the Colonial Funds since
                            February, 1998; Vice President since
                            February, 1998 of the Adviser (formerly
                            Senior Tax Manager, Coopers & Lybrand, LLP
                            from April, 1996 to January, 1998; Vice
                            President, 440 Financial Group/First Data
                            Investor Services Group from March, 1994 to
                            April, 1996; Vice President, The Boston
                            Company (subsidiary of Mellon Bank) from
                            December, 1993 to March, 1994; Assistant Vice    
                            President and Tax Manager, Mellon Bank from
                            March, 1992 to December, 1993).                  -0-

Michael H. Koonce           Secretary of the Fund and of the Colonial
(37)           1997         Funds since August, 1997 (formerly Assistant
                            Secretary from June, 1992 to July, 1997);
                            Director, Senior Vice President, General
                            Counsel, Clerk and Secretary of the Adviser
                            since August, 1997 (formerly Vice President,
                            Counsel, Assistant Secretary and Assistant
                            Clerk from June, 1992 to July, 1997); Vice
                            President - Legal and Clerk of TCG since
                            August, 1997 (formerly Assistant Clerk -         
                            Legal from April, 1993 to July, 1997).           -0-
</TABLE>

(3)      Except as otherwise noted, each individual has held the office
         indicated or other offices in the same company for the last five years.
(4)      On February 2, 1998, the Trustees and officers of the Fund as a group
         beneficially owned less than 1% of the then outstanding shares of the
         Fund.

                                       6

<PAGE>

                 Trustees' Compensation, Meetings and Committees

      The members of the Board of Trustees received the following compensation
from the Fund for the fiscal year ended October 31, 1997 and from the Colonial
Funds Complex for the calendar year ended December 31, 1997 for serving as
Trustees (5):

                           Aggregate                   Total Compensation From
                           Compensation From           Fund And Fund Complex
                           Fund For The Fiscal         Paid To The Trustees For
                           Year Ended                  The Calendar Year Ended
Trustee                    October 31, 1997            December 31, 1997 (6)
- -------                    ----------------            ---------------------

Robert J. Birnbaum         $1,042                      $ 93,949
Tom Bleasdale               1,191(7)                    106,432(8)
Lora S. Collins             1,045                        93,949
James E. Grinnell           1,076(9)                     94,698(10)
William D. Ireland, Jr.     1,133                       101,445
Richard W. Lowry            1,050                        94,698
William E. Mayer              994                        89,949
James L. Moody, Jr.         1,097(11)                    98,447(12)
John J. Neuhauser           1,053                        94,948
George L. Shinn             1,159                       103,443
Robert L. Sullivan          1,114                        99,945
Sinclair Weeks, Jr.         1,132                       101,445

(5)      The Fund does not currently provide pension or retirement plan benefits
         to the Trustees.
(6)      At December 31, 1997, the Colonial Funds Complex consisted of 39
         open-end and 5 closed-end management investment company portfolios.
(7)      Includes $697 payable in later years as deferred compensation. 
(8)      Includes $57,454 payable in later years as deferred compensation. 
(9)      Includes $28 payable in later years as deferred compensation. 
(10)     Includes $4,797 payable in later years as deferred compensation. 
(11)     Includes $1,097 payable in later years as deferred compensation. 
(12)     Total compensation of $98,447 for the calendar year ended December 31,
         1997 will be payable in later years a deferred compensation.

     The following table sets forth the amount of compensation paid to Messrs.
Birnbaum, Grinnell and Lowry in their capacities as Trustees or Directors of the
Liberty All-Star Equity Fund and of the Liberty All-Star Growth Fund, Inc.
(together, Liberty Funds) for service during the calendar year ended December
31, 1997:

                                       7

<PAGE>


                                 Total Compensation
                                 From Liberty Funds For
                                 The Calendar Year Ended
Trustee                          December 31, 1997(13)
- -------                          -----------------------
Robert J. Birnbaum                      $26,800
James E. Grinnell                        26,800
Richard W. Lowry                         26,800

(13)    The Liberty Funds are advised by Liberty Asset Management Company
        (LAMCO). LAMCO is an indirect wholly-owned subsidiary of Liberty
        Financial (an intermediate parent of the Adviser).

      During the Fund's fiscal year ended October 31, 1997, the Board of
Trustees held six meetings.

      The Audit Committee of the Colonial Funds, consisting of Messrs.
Bleasdale, Lowry, Moody, Sullivan and Weeks, met three times during the Fund's
fiscal year ended October 31, 1997. The Committee recommends to the Trustees the
independent accountants to serve as auditors, reviews with the independent
accountants the results of the auditing engagement and internal accounting
procedures and considers the independence of the independent accountants, the
range of their audit services and their fees.

      The Compensation Committee of the Colonial Funds, consisting of Ms.
Collins and Messrs. Grinnell, Neuhauser and Sullivan, met three times during the
Fund's fiscal year ended October 31, 1997. The Committee reviews compensation of
the Board of Trustees.

      The Governance Committee of the Colonial Funds, consisting of Messrs.
Bleasdale, Ireland, Moody, Neuhauser and Weeks, met three times during the
Fund's fiscal year ended October 31, 1997. The Committee in its sole discretion
recommends to the Trustees, among other things, nominees for Trustee and for
appointments to various committees. The Committee will consider candidates for
Trustee recommended by shareholders. Written recommendations with supporting
information should be directed to the Committee in care of the Fund.

      During the Fund's fiscal year ended October 31, 1997, each of the Trustees
attended more than 75% of the meetings of the Board of Trustees and the
committees of which such Trustee is a member.

      If any of the nominees listed above become unavailable for election, the
enclosed proxy may be voted for a substitute candidate in the discretion of the
proxy holder(s).

                                       8

<PAGE>

                                  Required Vote

      A plurality of the votes cast at the Meeting, if a quorum is represented,
is required for the election of each Trustee.

                           Description of the Adviser

      The Adviser is a wholly-owned subsidiary of TCG, which in turn is a
wholly-owned subsidiary of Liberty Financial. Liberty Financial is an indirect
majority-owned subsidiary of Liberty Mutual Insurance Company (Liberty Mutual).
Liberty Financial is a diversified and integrated asset management organization
which provides insurance and investment products to individuals and
institutions. Its principal executive offices are located at 600 Atlantic
Avenue, 24th Floor, Boston, Massachusetts 02210. Liberty Mutual is an
underwriter of workers' compensation insurance and a Massachusetts-chartered
mutual property and casualty insurance company. The principal business
activities of Liberty Mutual's subsidiaries other than Liberty Financial are
property-casualty insurance, insurance services and life insurance (including
group life and health insurance products) marketed through its own sales force.
Liberty Mutual's principal executive offices are located at 175 Berkeley Street,
Boston, Massachusetts 02117. Liberty Mutual is deemed to be the controlling
entity of the Adviser and its affiliates.

2.    Ratification of Independent Accountants.

      Price Waterhouse LLP was selected as independent accountants for the Fund
for the Fund's fiscal year ending October 31, 1998 by unanimous vote of the
Board of Trustees, subject to ratification or rejection by the shareholders.
Neither Price Waterhouse LLP nor any of its partners has any direct or material
indirect financial interest in the Fund. A representative of Price Waterhouse
LLP will be available at the Meeting, if requested by a shareholder in writing
at least five days before the Meeting, to respond to appropriate questions and
make a statement (if the representative desires).

                                  Required Vote

      Ratification requires the affirmative vote of a majority of the shares of
the Fund voted at the Meeting.

3.    Other Matters and Discretion of Attorneys Named in the Proxy.

      As of the date of this Proxy Statement, only the business mentioned in
Items 1 and 2 of the Notice of the Meeting is contemplated to be presented. If
any procedural or other matters properly come before the Meeting, the enclosed
proxy shall be voted in accordance with the best judgment of the proxy
holder(s).

                                       9

<PAGE>

      The Meeting is to be held at the same time as the meeting of shareholders
of Colonial Municipal Income Trust. It is anticipated that such meetings will be
held simultaneously. In the event that any Fund shareholder at the Meeting
objects to the holding of a simultaneous meeting and moves for an adjournment of
the meetings so that the Meeting of the Fund may be held separately, the persons
named as proxies will vote in favor of such an adjournment.

      If a quorum of shareholders (a majority of the shares entitled to vote at
the Meeting) is not represented at the Meeting or at any adjournment thereof,
or, even though a quorum is so represented, if sufficient votes in favor of the
Items set forth in the Notice of the Meeting are not received by April 29, 1998,
the persons named as proxies may propose one or more adjournments of the Meeting
for a period or periods of not more than ninety days in the aggregate and
further solicitation of proxies may be made. Any such adjournment may be
effected by a majority of the votes properly cast in person or by proxy on the
question at the session of the Meeting to be adjourned. The persons named as
proxies will vote in favor of such adjournment those proxies which they are
entitled to vote in favor of the Items set forth in the Notice of the Meeting.
They will vote against any such adjournment those proxies required to be voted
against any of such Items.

      Compliance with Section 16(a) of the Securities Exchange Act of 1934

      Section 16(a) of the Securities Exchange Act of 1934, as amended, and
Section 30(f) of the 1940 Act, as amended, require the Fund's Board of Trustees
and executive officers, persons who own more than ten percent of the Fund's
equity securities, the Fund's investment adviser and affiliated persons of the
Fund's investment adviser (Section 16 reporting persons), to file with the
Securities and Exchange Commission initial reports of ownership and reports of
changes in ownership of the Fund's shares and to furnish the Fund with copies of
all Section 16(a) forms they file. Based solely upon a review of copies of such
reports furnished to the Fund, and on representations that no other reports were
required during the fiscal year ended October 31, 1997, the Section 16 reporting
persons complied with all Section 16(a) filings applicable to them.

                    Date for Receipt of Shareholder Proposals

      Proposals of shareholders which are intended to be considered for
inclusion in the Fund's proxy statement relating to the 1999 Annual Meeting of
Shareholders of the Fund must be received by the Fund at One Financial Center,
Boston, Massachusetts 02111 on or before November 27, 1998.

    Shareholders are urged to vote, sign and mail their proxies immediately.

                                       10

<PAGE>







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                                       11

<PAGE>







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                                       12

<PAGE>



                     COLONIAL INTERMEDIATE HIGH INCOME FUND
                This Proxy is Solicited on Behalf of the Trustees


      The undersigned shareholder hereby appoints William J. Ballou, Harold W.
Cogger, Nancy L. Conlin and Michael H. Koonce and each of them, proxies of the
undersigned, with power of substitution, to vote at the Annual Meeting of
Shareholders of Colonial Intermediate High Income Fund, to be held at Boston,
Massachusetts, on Wednesday, April 29, 1998 and at any adjournments, as follows
on the reverse side:

/SEE REVERSE SIDE/ CONTINUED AND TO BE SIGNED ON REVERSE SIDE /SEE REVERSE SIDE/


/X/  Please mark votes as in this example.

This proxy when properly executed will be voted in the manner directed above
and, absent direction, will be voted for Items 1 and 2 listed below.

1.    ELECTION OF FIVE TRUSTEES.  (Item 1 of the Notice)

Nominees: Robert J. Birnbaum, James E. Grinnell, Richard W. Lowry, William E.
Mayer, Robert L. Sullivan

/  /  FOR ALL NOMINEES                        /  /  WITHHELD FROM ALL NOMINEES

/  /  For all nominees except as noted above

2.    PROPOSAL TO RATIFY THE SELECTION OF INDEPENDENT ACCOUNTANTS. 
(Item 2 of the Notice) 

               /  / FOR      /  / AGAINST     /  / ABSTAIN

3.    IN THEIR DISCRETION, UPON SUCH OTHER MATTERS AS MAY PROPERLY COME BEFORE 
THE MEETING.

MARK HERE FOR ADDRESS CHANGE AND NOTE AT LEFT /  /

PLEASE MARK, SIGN, DATE AND RETURN THIS PROXY PROMPTLY USING THE ENCLOSED
ENVELOPE.

                                   Please sign exactly as name appears
                                   hereon. When signing as attorney,
                                   executor, administrator, trustee or
                                   guardian, please give full title as
                                   such. If a corporation, please sign in
                                   full corporate name by President or
                                   other authorized officer. If a
                                   partnership, please sign in partnership
                                   name by authorized person.
                 


                                   Signature__________________ Date____________



                                   Signature__________________ Date____________




                        


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