<PAGE>
 
                                                                    Exhibit 25.7

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                                   FORM T-1

                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549

                           STATEMENT OF ELIGIBILITY
                  UNDER THE TRUST INDENTURE ACT OF 1939 OF A
                   CORPORATION DESIGNATED TO ACT AS TRUSTEE

                     CHECK IF AN APPLICATION TO DETERMINE
                     ELIGIBILITY OF A TRUSTEE PURSUANT TO
                       SECTION 305(b)(2)           |__|

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

                             THE BANK OF NEW YORK
              (Exact name of trustee as specified in its charter)


New York                                                13-5160382
(State of incorporation                                 (I.R.S. employer
if not a U.S. national bank)                            identification no.)

48 Wall Street, New York, N.Y.                          10286
(Address of principal executive offices)                (Zip code)


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


                       HOUSTON LIGHTING & POWER COMPANY
              (Exact name of obligor as specified in its charter)


Texas                                                   74-0694415
(State or other jurisdiction of                         (I.R.S. employer
incorporation or organization)                          identification no.)

1111 Louisiana
Houston, Texas                                          77002
(Address of principal executive offices)                (Zip code)

                            ______________________

                      Guarantee of Capital Securities of
                            HL&P Capital Trust III
                      (Title of the indenture securities)


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<PAGE>
 
1.   General information.  Furnish the following information as to the Trustee:

     (a) Name and address of each examining or supervising authority to which it
         is subject.

--------------------------------------------------------------------------------
               Name                                        Address
--------------------------------------------------------------------------------

     Superintendent of Banks of the State of       2 Rector Street, New York,
     New York                                      N.Y.  10006, and Albany, N.Y.
                                                   12203

     Federal Reserve Bank of New York              33 Liberty Plaza, New York,
                                                   N.Y.  10045

     Federal Deposit Insurance Corporation         Washington, D.C.  20429

     New York Clearing House Association           New York, New York  10005

     (b) Whether it is authorized to exercise corporate trust powers.

     Yes.

2.   Affiliations with Obligor.

     If the obligor is an affiliate of the trustee, describe each such
     affiliation.

     None.  (See Note on page 3.)

16.  List of Exhibits.

     Exhibits identified in parentheses below, on file with the Commission, are
     incorporated herein by reference as an exhibit hereto, pursuant to Rule 7a-
     29 under the Trust Indenture Act of 1939 (the "Act") and Rule 24 of the
     Commission's Rules of Practice.

     1.   A copy of the Organization Certificate of The Bank of New York
          (formerly Irving Trust Company) as now in effect, which contains the
          authority to commence business and a grant of powers to exercise
          corporate trust powers. (Exhibit 1 to Amendment No. 1 to Form T-1
          filed with Registration Statement No. 33-6215, Exhibits 1a and 1b to
          Form T-1 filed with Registration Statement No. 33-21672 and Exhibit 1
          to Form T-1 filed with Registration Statement No. 33-29637.)

4.   A copy of the existing By-laws of the Trustee.  (Exhibit 4 to Form T-1
     filed with Registration Statement No. 33-31019.)

                                      -2-
<PAGE>
 
     6.   The consent of the Trustee required by Section 321(b) of the Act.
          (Exhibit 6 to Form T-1 filed with Registration Statement No. 33-
          44051.)

     7.   A copy of the latest report of condition of the Trustee published
          pursuant to law or to the requirements of its supervising or examining
          authority.



                                     NOTE


     Inasmuch as this Form T-1 is filed prior to the ascertainment by the
Trustee of all facts on which to base a responsive answer to Item 2, the answer
to said Item is based on incomplete information.

     Item 2 may, however, be considered as correct unless amended by an
amendment to this Form T-1.



                                      -3-
<PAGE>
 
                                   SIGNATURE



     Pursuant to the requirements of the Act, the Trustee, The Bank of New York,
a corporation organized and existing under the laws of the State of New York,
has duly caused this statement of eligibility to be signed on its behalf by the
undersigned, thereunto duly authorized, all in The City of New York, and State
of New York, on the 10th day of January, 1997.


                                         THE BANK OF NEW YORK



                                         By:     /S/MARY JANE MORRISSEY
                                             --------------------------
                                             Name:  MARY JANE MORRISSEY
                                             Title: VICE PRESIDENT



                                      -4-
<PAGE>
 
 
                                                                       EXHIBIT 7

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                      Consolidated Report of Condition of

                             THE BANK OF NEW YORK
                    of 48 Wall Street, New York, N.Y. 10286
                   And Foreign and Domestic Subsidiaries,
a member of the Federal Reserve System, at the close of business September 30, 
1996 published in accordance with a call made by the Federal Reserve Bank of 
this District pursuant to the provisions of the Federal Reserve Act.

<TABLE> 
<CAPTION> 

                                                              Dollar Amounts
ASSETS                                                         in Thousands
<S>                                                           <C> 
Cash and balances due from depos-
 itory institutions:
 Noninterest-bearing balances and
   currency and coin.......................................     $ 4,404,522
 Interest-bearing balances.................................         732,833 
Securities:
 Held-to-maturity securities...............................         789,964
 Available-for-sale securities.............................       2,005,509
Federal funds sold in domestic offices 
 of the bank:
 Federal funds sold........................................       3,364,838
Loans and lease financing
 receivables:
 Loans and leases, net of unearned
  income...................28,728,602
 LESS: Allowance for loan and
  lease losses................584,525
 LESS: Allocated transfer risk
  reserve.........................429
 Loans and leases, net of unearned
  income, allowance, and reserve...........................      28,143,648
Assets held in trading accounts............................       1,004,242
Premises and fixed assets (including
  capitalized leases)......................................         605,668
Other real estate owned....................................          41,238
Investments in unconsolidated sub-
  sidiaries and associated 
  companies................................................         205,031
Customers' liability to this bank on 
  acceptances outstanding..................................         949,154
Intangible assets..........................................         490,524
Other assets...............................................       1,305,839
                                                                -----------
Total assets...............................................     $44,043,010
                                                                ===========
LIABILITIES
Deposits:
  In domestic offices......................................     $20,441,318
  Noninterest-bearing.......8,158,472
  Interest-bearing.........12,282,846
  In foreign offices, Edge and
  Agreement subsidiaries, and IBFs...                            11,710,903
  Noninterest-bearing......46,182
  Interest-bearing......11,664,721
Federal funds purchased in domes-
  tic offices of the bank
  Federal funds purchased..................................       1,565,288
Demand notes issued to the US
  Treasury.................................................         293,186
Trading liabilities........................................         826,856
Other borrowed money
  With original maturity of one year
    or less................................................       2,103,443
  With original maturity of more than
    one year...............................................          20,766
Bank's liability on acceptances exe-
  cuted and outstanding....................................         951,116
Subordinated notes and debentures..........................       1,020,400
Other liabilities..........................................       1,522,884
                                                                -----------
Total liabilities..........................................      40,456,160
                                                                -----------
EQUITY CAPITAL
Common stock...............................................         942,284
Surplus....................................................         525,666
Undivided profits and capital
  reserves.................................................       2,129,376
Net unrealized holding gains 
  (losses) on available-for-sale se-
  curities.................................................       (   2,073)
Cumulative foreign currency transla-
  tion adjustments.........................................       (   8,403)
                                                                -----------
Total equity capital.......................................       3,586,850
                                                                -----------
Total liabilities and equity 
  capital..................................................     $44,043,010
                                                                ===========

</TABLE> 
  I, Robert E. Keilman, Senior Vice President and Comptroller of the above-named
bank do hereby declare that this Report of Condition has been prepared in
conformance with the instructions issued by the Board of Governors of the
Federal Reserve System and is true to the best of my knowledge and belief.

                                                    Robert E. Keilman

  We, the undersigned directors, attest to the correctness of this Report of
Condition and declare that it has been examined by us and to the best of our
knowledge and belief has been prepared in conformance with the instructions
issued by the Board of Governors of the Federal Reserve System and is true and
correct.

                       )
  J. Carter Bacot      )
  Thomas A. Renyi      )    Directors
  Alan R. Griffith     )
                       )
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