COLONIAL INTERMEDIATE HIGH INCOME FUND
DEF 14A, 1997-03-26
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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 30, 1997



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 30, 1997, at 10:00 a.m. Eastern time, to:

       1.   Elect three Trustees;

       2.   Ratify or reject 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,

                              Arthur O. Stern, Secretary
March 26, 1997


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-85/471D-0397



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                                 PROXY STATEMENT
                               General Information

                                                                  March 26, 1997

    The enclosed proxy, which was first mailed on March 26, 1997, 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 3, 1997, the Fund had
outstanding 14,587,959.449 shares of beneficial interest. Shareholders of record
at the close of business on February 3, 1997 will have one vote for each share
held. As of February 3, 1997, The Depository Trust Company (Cede & Co.), 7
Hanover Square, New York, New York 10004, owned of record 99.85% 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
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1.  Election of Three Trustees.

    Messrs. Moody, Shinn and Weeks (who have each agreed to serve) are proposed
for election as Trustees of the Fund, each to serve for three years or until a
successor is elected. The Board of Trustees consists of Ms. Collins and Messrs.
Birnbaum, Bleasdale, Grinnell, Ireland, Lowry, Mayer, Moody, Neuhauser, Shinn,
Sullivan and Weeks. 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):

               1998              1999              2000
               ----              ----              ----
                                                   
               Mr. Birnbaum      Mr. Bleasdale     Mr. Moody
               Mr. Grinnell      Ms. Collins       Mr. Shinn
               Mr. Lowry         Mr. Ireland       Mr. Weeks
               Mr. Mayer         Mr. Neuhauser     
               Mr. Sullivan                        
                                               
    The following table sets forth certain information about the Board of
Trustees:

                                                           Shares   
                                                        Beneficially
                                                         Owned and 
                                                          Percent   
                                                        of Fund at
Name       Trustee       Principal Occupation(1) and     February
(Age)      Since                Directorships           3, 1997 (2)
                                                         
Robert J. Birnbaum       Retired (formerly Special          ----
(69)          1995       Counsel, Dechert Price &
                         Rhoads--law). Director or
                         Trustee: Colonial Funds,
                         Liberty All-Star Equity Fund,
                         Liberty All-Star Growth Fund,
                         Inc. (formerly The Charles
                         Allmon Trust, Inc.), The
                         Emerging Germany Fund.
                                                         
Tom Bleasdale            Retired (formerly Chairman of      ----
(66)          1988       the Board and Chief Executive
                         Officer, Shore Bank & Trust
                         Company--banking). Director or
                         Trustee: Colonial Funds, The
                         Empire Company.
                                                         
Lora S. Collins          Attorney (formerly Attorney,       ----
(61)          1988       Kramer, Levin, Naftalis,
                         Nessen, Kamin & Frankel--law).
                         Trustee: Colonial Funds.
                     
                                       3
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                                                           Shares   
                                                        Beneficially
                                                         Owned and 
                                                          Percent   
                                                        of Fund at
Name       Trustee       Principal Occupation(1) and     February
(Age)      Since                Directorships           3, 1997 (2)

James E. Grinnell        Private Investor. Director or      ----
(67)         1995        Trustee: Colonial Funds,
                         Liberty All-Star Equity Fund,
                         Liberty All-Star Growth Fund,
                         Inc. (formerly The Charles
                         Allmon Trust, Inc.).

William D. Ireland, Jr.  Retired. Trustee: Colonial         ----
(73)         1992        Funds.

Richard W. Lowry         Private Investor. Director or      ----
(60)        1995         Trustee: Colonial Funds,
                         Liberty All-Star Equity Fund,
                         Liberty All-Star Growth Fund,
                         Inc. (formerly The Charles
                         Allmon Trust, Inc.).

William E. Mayer*        Partner, Development Capital,      ----
(56)        1994         LLC (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,
                         Schuller Corp.

James L. Moody, Jr.      Chairman of the Board and          ----
(65)        1988         Director, Hannaford Bros. Co.
                         (food distributor) (formerly
                         Chief Executive Officer,
                         Hannaford Bros. Co.). Director
                         or Trustee: Colonial Funds,
                         Penobscot Shoe Co., Staples,
                         Inc., UNUM Corporation, IDEXX
                         Laboratories, Inc., Sobeys, Inc.

John J. Neuhauser        Dean of the School of              ----
(53)        1992         Management, Boston College
                         (higher education). Director or
                         Trustee: Colonial Funds, Hyde
                         Athletic Industries, Inc.

George L. Shinn          Financial Consultant (formerly     ----
(74)        1992         Chairman, Chief Executive
                         Officer and Consultant, The
                         First Boston
                         Corporation--holding company).
                         Director or Trustee: Colonial
                         Funds, The New York Times
                         Company.

Robert L. Sullivan       Retired Partner, Peat Marwick      ----
(69)        1989         Main & Co. (management
                         consulting) (formerly
                         self-employed Management
                         Consultant.) Trustee: Colonial
                         Funds.

                                       4
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                                                           Shares   
                                                        Beneficially
                                                         Owned and 
                                                          Percent   
                                                        of Fund at
Name       Trustee       Principal Occupation(1) and     February
(Age)      Since                Directorships           3, 1997 (2)

Sinclair Weeks, Jr.      Chairman of the Board, Reed &      ----
(73)        1992         Barton Corporation (metal
                         products). Trustee: Colonial
                         Funds.

*     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 3, 1997, 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.

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


          Executive
Name      Officer        Office with Fund; Principal
(Age)     Since          Occupation (3)

Harold W. Cogger         President of the Fund and of
(61)        1993         the Colonial Funds (formerly
                         Vice President); Chairman of
                         the Board and Director of the
                         Adviser (formerly President,
                         Chief Executive Officer and
                         Executive Vice President);
                         Director and Chairman of the
                         Board of The Colonial Group,
                         Inc. (TCG) (formerly
                         President and Chief Executive
                         Officer); Executive Vice
                         President and Director of
                         Liberty Financial Companies,
                         Inc. (Liberty Financial);
                         Director or Trustee: Liberty
                         All-Star Equity Fund, Liberty
                         All-Star Growth Fund, Inc.
                         (formerly The Charles Allmon
                         Trust, Inc.), Stein Roe &
                         Farnham Incorporated.


                                       5
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          Executive
Name      Officer        Office with Fund; Principal
(Age)     Since          Occupation (3)

Davey S. Scoon           Vice President of the Fund
(50)      1993           and of the Colonial Funds
                         (formerly Treasurer);
                         Executive Vice President and 
                         Director of the Adviser
                         (formerly Senior Vice 
                         President and Treasurer);
                         Executive Vice President and 
                         Chief Operating Officer of
                         TCG (formerly Vice President 
                         - Finance and Administration 
                         and Treasurer).

Carl C. Ericson          Vice President of the Fund;
(53)      1989           Senior Vice President,
                         Director and Manager of the
                         Taxable Fixed Income Group of
                         the Adviser (formerly Vice
                         President).

Andrea S. Feingold       Vice President of the Fund
(33)      1993           (formerly Assistant
                         Treasurer); Vice President
                         and head of the Corporate
                         Group of the Adviser
                         (formerly Assistant Vice
                         President and Analyst of the
                         Adviser); formerly Investment
                         Analyst, Sun Financial Group.

Timothy J. Jacoby        Treasurer and Chief Financial
(44)      1996           Officer of the Fund and of
                         the Colonial Funds; Senior
                         Vice President of the
                         Adviser; (formerly Senior
                         Vice President, Fidelity
                         Accounting and Custody
                         Services and Assistant
                         Treasurer to the Fidelity
                         Group of Funds).

Peter L. Lydecker        Chief Accounting Officer and
(43)      1993           Controller of the Fund and of
                         the Colonial Funds (formerly
                         Assistant Controller); Vice
                         President of the Adviser
                         (formerly Assistant Vice
                         President).

Arthur O. Stern          Secretary of the Fund and of
(58)      1988           the Colonial Funds; Director,
                         Executive Vice President,
                         General Counsel, Clerk and 
                         Secretary of the Adviser;
                         Executive Vice President 
                         Legal and Clerk of TCG
                         (formerly Executive Vice 
                         President - Compliance and
                         Vice President - Legal).


(3)   Except as otherwise noted, each individual has held the office indicated
      or other offices in the same company for the last five years.

                                       6
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                    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, 1996 and from the Colonial
Funds complex for the calendar year ended December 31, 1996 for serving as
Trustees (4):


                                             Total
                                             Compensation
                         Aggregate           From Fund And
                         Compensation        Fund Complex
                         From Fund For       Paid To The
                         The Fiscal          Trustees For The
                         Year Ended          Calendar Year
                         October 31,         Ended December
Trustee                  1996                31, 1996 (5)
- --------                 -------------       ------------------
Robert J. Birnbaum       $1,166             $ 92,000
Tom Bleasdale             1,322 (6)          104,500(7)
Lora S. Collins           1,168               92,000
James E. Grinnell         1,179               93,000
William D. Ireland, Jr.   1,435              109,000
Richard W. Lowry          1,194               95,000
William E. Mayer          1,151               91,000
James  L. Moody,          1,345 (8)          106,500(9)
John J. Neuhauser         1,195               94,500
George L. Shinn           1,339              105,500
Robert L. Sullivan        1,279              102,000
Sinclair Weeks, Jr.       1,393              110,000

(4) The Fund does not currently provide pension or retirement plan benefits to
    the Trustees.

(5) At December 31, 1996, the Colonial Funds complex consisted of 37 open-end
    and 5 closed-end management investment portfolios.

(6) Includes $651 payable in later years as deferred compensation.

(7) Includes $51,000 payable in later years as deferred compensation.

(8) Total compensation of $1,345 for the fiscal year ended October 31, 1996,
    will be payable in later years as deferred compensation.

(9) Total compensation of $106,500 for the calendar year ended December 31,
    1996, will be payable in later years as 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.
(formerly The Charles Allmon Trust, Inc.) (together, Liberty Funds) for service
during the calendar year ended December 31, 1996:

                                       7
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                      Total Compensation
                      From Liberty Funds For
                      The Calendar Year Ended
Trustee               December 31, 1996(10)
- --------              ------------------------
Robert J. Birnbaum           $25,000
James E. Grinnell             25,000
Richard W. Lowry              25,000

(10) At December 31, 1996, the Liberty Funds were 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, 1996, the Board of Trustees
held six meetings.

    The Audit Committee of the Colonial Funds, consisting of Messrs. Bleasdale,
Ireland, Lowry, Moody, Shinn, Sullivan and Weeks, met three times during the
Fund's fiscal year ended October 31, 1996. 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 controls, 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. Neuhauser, Sullivan and Weeks, met once during the Fund's fiscal
year ended October 31, 1996. The Committee reviews compensation of the Board of
Trustees.

    The Nominating Committee of the Colonial Funds, consisting of Messrs.
Bleasdale, Ireland, Moody and Weeks, did not meet during the Fund's fiscal year
ended October 31, 1996. The Committee in its sole discretion recommends to the
Trustees 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, 1996, 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
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                                  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
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, 1997, 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
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    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 30, 1997,
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, 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 filings that were so furnished to
the Fund, the Fund believes that Stephen E. Gibson, President, Chief Executive
Officer and a Director of the Adviser and TCG, filed a late Form 3 (Initial
Statement of Beneficial Ownership), on which he reported no holdings of the
Fund.

                    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 1998 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, 1997.

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


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                                       11
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                                       12


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

PROXY

      The undersigned shareholder hereby appoints Harold W. Cogger, Nancy L.
Conlin, Michael H. Koonce, and Arthur O. Stern, 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 30, 1997 and at any adjournments, as follows
on the 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 THREE TRUSTEES. (Item 1 of the Notice)

      James L. Moody, Jr.     George L. Shinn         Sinclair Weeks, Jr.

FOR the nominees listed below (except as marked to the contrary below) / /

/ /  WITHHOLD AUTHORITY to vote for the nominees listed

/ /________________________________________________________________________ 
INSTRUCTION: To withhold authority to vote for any individual nominee write
that nominee's name on the line.

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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