<PAGE>   1
                  THIS CONFORMING PAPER FORMAT DOCUMENT IS BEING SUBMITTED
 PURSUANT TO RULE 901(d) OF REGULATION S-T


                                                                    EXHIBIT 25-H

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


                                    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)


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



                           PHILLIPS PETROLEUM COMPANY
               (Exact name of obligor as specified in its charter)


Delaware                                                   73-0400345
(State or other jurisdiction of                            (I.R.S. employer
incorporation or organization)                             identification no.)


Phillips Building
Bartlesville, Oklahoma                                     74004
(Address of principal executive offices)                   (Zip code)

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


           Guarantees of Preferred Securities of Phillips 66 Capital V
                       (Title of the indenture securities)






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


<PAGE>   2


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.

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 17 C.F.R.
    229.10(d).

    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>   3

    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.







                                      -3-


<PAGE>   4




                                    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 21st day of May, 1998.


                                          THE BANK OF NEW YORK



                                          By:    /s/ VAN K. BROWN
                                             --------------------------------- 
                                             Name:  VAN K. BROWN
                                             Title: ASSISTANT VICE PRESIDENT



                                       -4-

<PAGE>   5
                                                                    EXHIBIT 25-H

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

                     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 December 31,
1997, 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 .....................................................        $ 5,742,986
  Interest-bearing balances ..............................................          1,342,769
Securities:
  Held-to-maturity securities ............................................          1,099,736
  Available-for-sale securities ..........................................          3,882,686
Federal funds sold and Securities pur-
  chased under agreements to resell.......................................          2,568,530
Loans and lease financing
  receivables:
  Loans and leases, net of unearned
    income .................35,019,608
  LESS: Allowance for loan and
    lease losses ..............627,350
  LESS: Allocated transfer risk
    reserve..........................0
  Loans and leases, net of unearned
    income, allowance, and reserve........................................         34,392,258
Assets held in trading accounts ..........................................          2,521,451
Premises and fixed assets (including
  capitalized leases) ....................................................            659,209
Other real estate owned ..................................................             11,992
Investments in unconsolidated
  subsidiaries and associated
  companies ..............................................................            226,263
Customers' liability to this bank on
  acceptances outstanding ................................................          1,187,449
Intangible assets ........................................................            781,684
Other assets .............................................................          1,736,574
                                                                                  -----------
Total assets .............................................................        $56,153,587
                                                                                  ===========

LIABILITIES
Deposits:
  In domestic offices ....................................................        $27,031,362
  Noninterest-bearing ......11,899,507
  Interest-bearing .........15,131,855
  In foreign offices, Edge and
  Agreement subsidiaries, and IBFs .......................................         13,794,449
  Noninterest-bearing .........590,999
  Interest-bearing .........13,203,450
Federal funds purchased and Securities
  sold under agreements to repurchase.....................................          2,338,881
Demand notes issued to the U.S.
  Treasury ...............................................................            173,851
Trading liabilities ......................................................          1,695,216
Other borrowed money:
  With remaining maturity of one year
    or less ..............................................................          1,905,330
  With remaining maturity of more than
    one year through three years..........................................                  0
  With remaining maturity of more than
    three years ..........................................................             25,664
Bank's liability on acceptances exe-
  cuted and outstanding ..................................................          1,195,923
Subordinated notes and debentures ........................................          1,012,940
Other liabilities ........................................................          2,018,960
                                                                                  -----------
Total liabilities ........................................................         51,192,576
                                                                                  -----------

EQUITY CAPITAL
Common stock .............................................................          1,135,284
Surplus ..................................................................            731,319
Undivided profits and capital
  reserves ...............................................................          3,093,726
Net unrealized holding gains
  (losses) on available-for-sale
  securities .............................................................             36,866
Cumulative foreign currency transla-
  tion adjustments .......................................................            (36,184)
                                                                                  -----------
Total equity capital .....................................................          4,961,011
                                                                                  -----------
Total liabilities and equity
  capital ................................................................        $56,153,587
                                                                                  ===========
</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.


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

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