
<PAGE>   1

                                                                   Exhibit 10.1

================================================================================



                       UNITED ASSET MANAGEMENT CORPORATION




                       -----------------------------------

                                 FIRST AMENDMENT
                            Dated as of June 23, 1998



                                       to



                            NOTE PURCHASE AGREEMENTS
                           Dated as of August 1, 1995

                       -----------------------------------




                   Re: $150,000,000 7.12% Senior Secured Notes
                               Due August 25, 2005








================================================================================


<PAGE>   2


                   FIRST AMENDMENT TO NOTE PURCHASE AGREEMENTS

     THIS FIRST AMENDMENT dated as of June 23, 1998 (this "First Amendment") to
the Note Purchase Agreements, each dated as of August 1, 1995 is between UNITED
ASSET MANAGEMENT CORPORATION, a Delaware corporation (the "Company"), and each
of the institutions which is a signatory to this First Amendment (collectively,
the "Noteholders").


                                    RECITALS:

     A. The Company and each of the Noteholders have heretofore entered into
separate and several Note Purchase Agreements, each dated as of August 1, 1995
(collectively, the "Note Purchase Agreements"). The Company has heretofore
issued the $150,000,000 7.12% Senior Secured Notes Due August 25, 2005 (the
"Existing Notes") dated August 25, 1995 pursuant to the Note Purchase
Agreements.

     B. The Company and the Noteholders now desire to amend the Note Purchase
Agreements in the respects, but only in the respects, hereinafter set forth.

     C. Capitalized terms used herein shall have the respective meanings
ascribed thereto in the Note Purchase Agreements unless herein defined or the
context shall otherwise require.

     D. All requirements of law have been fully complied with and all other acts
and things necessary to make this First Amendment a valid, legal and binding
instrument according to its terms for the purposes herein expressed have been
done or performed.

     NOW, THEREFORE, upon the full and complete satisfaction of the conditions
precedent to the effectiveness of this First Amendment set forth in Section 3.1
hereof, and in consideration of good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Company and the Noteholders do
hereby agree as follows:


SECTION 1. AMENDMENTS.

          1.1. Section 9.7 of the Note Purchase Agreements shall be and is
hereby amended in its entirety to read as follows:

          "Section 9.7. Intentionally Omitted"

          1.2. Section 10.4(a)(v) of the Note Purchase Agreements shall be and
is hereby amended in its entirety to read as follows:


<PAGE>   3


          "(v) additional Funded Debt of the Company and/or any one or more of
its Subsidiaries, provided that at the time of creation, issuance, assumption,
guarantee or incurrence thereof and after giving effect thereto and to the
application of the proceeds thereof:

               (A) Consolidated Operating Cash Flow for the immediately
          preceding four fiscal quarters will be at least equal to the relevant
          percentage of Consolidated Senior Funded Debt hereinafter specified
          during the applicable period set forth below:

--------------------------------------------------------------------------------
                                        Consolidated Operating Cash Flow
     If Funded Debt is Incurred            as a Minimum Percentage of
         During the Period:             Consolidated Senior Funded Debt:
     --------------------------         --------------------------------        
--------------------------------------------------------------------------------

--------------------------------------------------------------------------------
   June 23, 1998 to and including                    15.0%
        December 31, 1999
--------------------------------------------------------------------------------

  January 1, 2000 to and including                   18.0%
        December 31, 2000
--------------------------------------------------------------------------------

   January 1, 2001 and thereafter                    20.0%
--------------------------------------------------------------------------------

          and

               (B) Consolidated Operating Cash Flow for the immediately
          preceding four fiscal quarters will be at least equal to the relevant
          percentage of Consolidated Funded Debt hereinafter specified during
          the applicable period set forth below:


--------------------------------------------------------------------------------
                                        Consolidated Operating Cash Flow
      If Funded Debt is Incurred           as a Minimum Percentage of
          During the Period:               Consolidated Funded Debt:
      --------------------------        --------------------------------        
--------------------------------------------------------------------------------

--------------------------------------------------------------------------------
    June 23, 1998 to and including                   12.0%
         December 31, 1998
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

   January 1, 1999 to and including                  13.5%
        December 31, 1999
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

    January 1, 2000 and thereafter                   15.0%
--------------------------------------------------------------------------------


                                      -3-


<PAGE>   4




          and

               (C) in the case of the issuance of any Funded Debt of the Company
          secured by Liens permitted by Section 10.5(k) and any Funded Debt of a
          Subsidiary, the sum of (y) the aggregate amount of all Funded Debt
          secured by Liens permitted by Section 10.5(k) plus (z) the aggregate
          amount of all Funded Debt of Subsidiaries, shall not exceed
          $63,000,000;".

          1.3. Section 7.2(a) of the Note Purchase Agreements shall be and is
hereby amended by deleting the reference to "9.7," therefrom.

          1.4. Section 11.1(c) of the Note Purchase Agreements shall be and is
hereby amended by deleting the reference to "9.7," therefrom.

          1.5. From and after June 23, 1998 interest on the Notes shall accrue
at the rate of 8.92% per annum.


SECTION 2. EXCHANGE OF NOTES.

          2.1. The Company agrees to issue and deliver amended notes not later
than July 10, 1998 in the form of Exhibit 1 to the Note Purchase Agreements (the
"Amended Notes") to the Noteholders in exchange for their outstanding
corresponding Existing Notes. The Noteholders agree to surrender their Existing
Notes to the Company (c/o Chapman and Cutler) in exchange for the Amended Notes,
and upon surrender, the Existing Notes shall be canceled by the Company and
shall be void. The Company shall pay any stamp tax or governmental charge
imposed upon such exchange.

          2.2. Each Amended Note shall be in the form of a single registered
Note, shall be registered in the name of the Noteholder surrendering such
Existing Note as reflected on the books and records of the Company, shall be
issued for the same principal amount as the outstanding principal amount of the
Existing Note surrendered in exchange therefor.

          2.3. The Company shall not later than July 10, 1998 deliver the
Amended Notes in proper form at the offices of Chapman and Cutler, 111 West
Monroe Street, Chicago, Illinois 60603, to be held by such firm for delivery
against surrender by the Noteholders in exchange therefor of the Existing Notes.

          2.4. Each of the Noteholders and the Company agrees that the
amendments effected pursuant to this First Amendment and the exchange of Amended
Notes for Existing Notes pursuant to this First Amendment shall not be deemed a
prepayment, redemption or 

                                      -4-


<PAGE>   5


repurchase of the Existing Notes for any purpose, including Section 8 of the
Note Purchase Agreements.


SECTION 3. REPRESENTATIONS AND WARRANTIES OF THE COMPANY.

          3.1. To induce the Noteholders to execute and deliver this First
Amendment (which representations shall survive the execution and delivery of
this First Amendment), the Company represents and warrants to the Noteholders
that:

               (a) this First Amendment has been duly authorized, executed and
          delivered by it and this First Amendment constitutes the legal, valid
          and binding obligation, contract and agreement of the Company
          enforceable against it in accordance with its terms, except as
          enforcement may be limited by bankruptcy, insolvency, reorganization,
          moratorium or similar laws or equitable principles relating to or
          limiting creditors' rights generally;

               (b) the Note Purchase Agreements, as amended by this First
          Amendment, constitute the legal, valid and binding obligations,
          contracts and agreements of the Company enforceable against it in
          accordance with their respective terms, except as enforcement may be
          limited by bankruptcy, insolvency, reorganization, moratorium or
          similar laws or equitable principles relating to or limiting
          creditors' rights generally;

               (c) the execution, delivery and performance by the Company of
          this First Amendment (i) has been duly authorized by all requisite
          corporate action and, if required, shareholder action, (ii) does not
          require the consent or approval of any governmental or regulatory body
          or agency, and (iii) will not (A) violate (1) any provision of law,
          statute, rule or regulation or its certificate of incorporation or
          bylaws, (2) any order of any court or any rule, regulation or order of
          any other agency or government binding upon it, or (3) any provision
          of any material indenture, agreement or other instrument to which it
          is a party or by which its properties or assets are or may be bound,
          including, without limitation, the Bank Credit Agreement, or (B)
          result in a breach or constitute (alone or with due notice or lapse of
          time or both) a default under any indenture, agreement or other
          instrument referred to in clause (iii)(A)(3) of this Section 3.1(c);
          and

               (d) as of the date hereof and after giving effect to this First
          Amendment, no Default or Event of Default has occurred which is
          continuing.


SECTION 4. CONDITIONS TO EFFECTIVENESS OF THIS FIRST AMENDMENT; CERTAIN CLOSING
           CONDITIONS.


                                      -5-


<PAGE>   6


          4.1. Executed counterparts of this First Amendment, duly executed by
the Company and the holders of at least 51% of the outstanding principal of the
Notes (exclusive of Notes owned by the Company or any of its Affiliates), having
been delivered, this First Amendment shall become and be effective on and as of
June 23, 1998.

          4.2. Not later than July 10, 1998, each and everyone of the following
conditions shall have been satisfied:

               (a) the Noteholders shall have received a copy of the resolutions
          of the Board of Directors of the Company authorizing the execution,
          delivery and performance by the Company of this First Amendment,
          certified by its Secretary or an Assistant Secretary;

               (b) The Noteholders shall have received a certificate of an
          Responsible Officer of the Company to the effect that the
          representations and warranties of the Company set forth in Section 3
          hereof are true and correct on and with respect to the date hereof;
          and

               (c) the Noteholders shall have received the favorable opinion of
          counsel to the Company as to the matters set forth in Sections 3.1(a),
          3.1(b) and 3.1(c) hereof, which opinion shall be in form and substance
          satisfactory to the Noteholders.


SECTION 5. PAYMENT OF NOTEHOLDERS' COUNSEL FEES AND EXPENSES.

               The Company agrees to pay upon demand the reasonable fees and
expenses of Chapman and Cutler, counsel to the Noteholders, in connection with
the negotiation, preparation, approval, execution and delivery of this First
Amendment.


SECTION 6. MISCELLANEOUS.

          6.1. This First Amendment shall be construed in connection with and as
part of each of the Note Purchase Agreements, and except as modified and
expressly amended by this First Amendment, all terms, conditions and covenants
contained in the Note Purchase Agreements and the Notes are hereby ratified and
shall be and remain in full force and effect.

          6.2. Any and all notices, requests, certificates and other instruments
executed and delivered after the execution and delivery of this First Amendment
may refer to the Note Purchase Agreements without making specific reference to
this First Amendment but nevertheless all such references shall include this
First Amendment unless the context otherwise requires.


                                     -6-


<PAGE>   7


          6.3. The descriptive headings of the various Sections or parts of this
First Amendment are for convenience only and shall not affect the meaning or
construction of any of the provisions hereof.

          6.4. This First Amendment shall be governed by and construed in
accordance with the laws of the Commonwealth of Massachusetts (excluding
choice-of-law principles of the law of such State that would require the
application of the laws of a jurisdiction other than such State) and shall take
effect as a sealed instrument in accordance with such laws.

          6.5. The execution hereof by you shall constitute a contract between
us for the uses and purposes hereinabove set forth, and this First Amendment may
be executed in any number of counterparts, each executed counterpart
constituting an original, but all together only one agreement.

                                                 UNITED ASSET MANAGEMENT 
                                                      CORPORATION


                                             By   /s/ William H. Park
                                                  -----------------------------
                                                  Executive Vice President and
                                                  Chief Financial Officer



Accepted and Agreed to as of June 23, 1998:


                                             ALLSTATE LIFE INSURANCE COMPANY

                                             By   /s/ Charles D. Mires
                                                  -----------------------------
                                                  Charles D. Mires

                                             By   /s/ Robert B. Bodett
                                                  -----------------------------
                                                  Robert B. Bodett
                                                    Authorized Signatories


                                      -7-


<PAGE>   8


                                     PROVIDENT LIFE AND ACCIDENT INSURANCE   
                                       COMPANY

                                     By:  Provident Investment Management, LLC, 
                                        Its Agent

                                     By   /s/ David Fussell
                                          -----------------------------
                                              David Fussell
                                              Agent

                                     THE TRAVELERS INSURANCE COMPANY

                                     By   /s/ Pamela Westmoreland
                                          -----------------------------
                                              Pamela Westmoreland
                                              Investment Officer

                                     CM LIFE INSURANCE COMPANY

                                     By   /s/ Richard E. Spencer II
                                          -----------------------------
                                              Richard E. Spencer II
                                              Managing Director

                                     CONNECTICUT MUTUAL LIFE INSURANCE 
                                      COMPANY

                                     By:   Massachusetts Mutual Life Insurance 
                                           Company As Successor In Interest

                                     By   /s/ Richard E. Spencer II
                                          -----------------------------
                                              Richard E. Spencer II
                                              Managing Director


                                     MASSACHUSETTS MUTUAL LIFE INSURANCE 
                                      COMPANY

                                     By   /s/ Richard E. Spencer II
                                          -----------------------------
                                              Richard E. Spencer II
                                              Managing Director


                                      -8-


<PAGE>   9


                                     OXFORD LIFE INSURANCE COMPANY

                                     By:   Lincoln Investment Management, Inc., 
                                           Its Attorney-In-Fact

                                     By   /s/ J. Steven Staggs
                                          -----------------------------
                                              J. Steven Staggs
                                               Vice President

                                     THE LINCOLN NATIONAL LIFE INSURANCE 
                                       COMPANY

                                     By:   Lincoln Investment Management, Inc., 
                                           Its Attorney-In-Fact

                                     By   /s/ J. Steven Staggs
                                          -----------------------------
                                              J. Steven Staggs
                                              Vice President

                                     LINCOLN NATIONAL REINSURANCE COMPANY 
                                      (BARBADOS) LTD.

                                     By:   Lincoln Investment Management, Inc., 
                                           Its Attorney-In-Fact

                                     By   /s/ J. Steven Staggs
                                          -----------------------------
                                              J. Steven Staggs
                                               Vice President

                                     LONDON LIFE INTERNATIONAL REINSURANCE 
                                       CORPORATION

                                     By:   Lincoln Investment Management, Inc., 
                                           Its Attorney-In-Fact

                                     By   /s/ J. Steven Staggs
                                          -----------------------------     
                                              J. Steven Staggs
                                              Vice President


                                      -9-
