<PAGE>
 
                                                                   EXHIBIT 10.40

            FIRST AMENDMENT TO LIMITED LIABILITY COMPANY AGREEMENT
            ------------------------------------------------------

     This First Amendment to Limited Liability Company Agreement (the 
"Amendment") is entered into as of March 31, 1997 by and between G&L Realty 
Partnership, L.P., a Delaware limited partnership ("G&L") and Property 
Acquisition Trust I, a Delaware business trust ("PAT") for the purpose of 
amending that certain Limited Liability Company Agreement (the "Agreement") of 
GLN Capital Co., LLC (the "Company") dated as of November 25, 1996.  All 
capitalized terms not defined herein shall have the same meanings set forth in 
the Agreement.

                                  Background
                                  ----------

     G&L and PAT have formed the Company on the terms stated in the Agreement.  
G&L and PAT desire to amend the Agreement in certain respects in connection with
the acquisition of (i) those certain Massachusetts Industrial Finance Authority 
Health Care Revenue Bonds (Hampden Nursing Homes, Inc. Project) Series 1989A(the
"1989A Bonds"), and (ii) those certain Massachusetts Industrial Finance Agency 
Health Care Revenue Bonds (Hampden Nursing Homes, Inc. Project) Series 1989B
(the "1989B Bonds", and together with the 1989A Bonds, the "Bonds") by the
Company.





<PAGE>
 
     NOW, THEREFORE, intending to be legally bound, the parties agree as
follows:

                       Approval of Acquisition of Bonds
                       --------------------------------

     The Members consent to the acquisition of the Bonds by the Company.

                    Preferred Return With Respect to Bonds
                    --------------------------------------

     Notwithstanding anything to the contrary contained in the Agreement, (i) 
the Preferred Return on PAT's Preferred Capital Amount resulting from its 
Capital Contribution with respect to the acquisition of the Bonds and (ii) the 
interest rate on the NACC Loan on funds advanced by NACC to the Company to 
acquire the Bonds shall be as follows:

     Annual Period                           Preferred Return/
     -------------                           -----------------
                                               Interest Rate
                                             -----------------

     4/1/97 - 3/31/98                        12%
     4/1/98 - 3/31/99                        15%
     4/1/99 and thereafter                   20%

     Except as herein amended, the Agreement shall continue in full force and 
effect, provided that the Members shall execute any agreements or other 
amendments to the Agreement as are necessary to effect the purposes of this 
Amendment.






<PAGE>
 
                             Capital Contributions
                             ---------------------

     Notwithstanding anything in the Agreement to the contrary, PAT's capital 
contributions with respect to the Bonds shall consist of $1,500,000.00 and G&L's
capital contribution with respect to the Bonds shall consist of $3,165,000.00. 
Pursuant to Section 3.7 of the Agreement NACC shall make a loan to the Company 
with respect to the Bonds in the amount of $3,000,000.00.

     This Amendment may be signed in several counterparts, each of which shall 
be deemed an original, but all of which shall constitute one and the same 
instrument.  Facsimile signatures shall be binding upon the signatories.

                                       G&L REALTY PARTNERSHIP, L.P.

                                       By: G&L Realty Corp.,
                                            as General Partner




                                       By: /s/ Daniel Gottlieb
                                           --------------------------------
                                           Name: Daniel Gottlieb
                                           Title: CEO


                                       PROPERTY ACQUISITION TRUST I



                                       By: 
                                           ---------------------------------
                                           Name:
                                           Title:

                   [Signatures continued on following page]





<PAGE>
 

Consented to:                            NOMURA ASSET CAPITAL
                                         CORPORATION

                                         By:
                                            --------------------------------
                                              Name:
                                              Title:
<PAGE>
 
                             Capital Contributions
                             ---------------------

     Notwithstanding anything in the Agreement to the contrary, PAT's capital 
contributions with respect to the Bonds shall consist of $1,500,000.00 and G&L's
capital contribution with respect to the Bonds shall consist of $3,165,000.00. 
Pursuant to Section 3.7 of the Agreement NACC shall make a loan to the Company 
with respect to the Bonds in the amount of $3,000,000.00.

     This Amendment may be signed in several counterparts, each of which shall 
be deemed an original, but all of which shall constitute one and the same 
instrument.  Facsimile signatures shall be binding upon the signatories.

                                       G&L REALTY PARTNERSHIP, L.P.

                                       By: G&L Realty Corp.,
                                            as General Partner


                                       By: 
                                          ------------------------------------
                                          Name:
                                          Title:



                                       PROPERTY ACQUISITION TRUST I


                                       By: /s/ Sheryl McAfee
                                          ------------------------------------
                                          Name:   SHERYL McAFEE
                                          Title:  DESIGNATED OFFICER

                   [Signatures continued on following page]


<PAGE>
 
Consented to:                          NOMURA ASSET CAPITAL
                                       CORPORATION

 
                                       By: /s/ Ray Anthony
                                           ---------------------------------
                                             Name: Ray Anthony
                                             Title: