SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                                   FORM 10-Q

[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE
    ACT OF 1934 FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1998

                                       OR

[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE
    ACT OF 1934 FOR THE TRANSITION PERIOD FROM _______________ TO ______________

                         COMMISSION FILE NUMBER: 0-6910

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

                               TEL OFFSHORE TRUST
             (Exact Name of Registrant as Specified in its Charter)

                 TEXAS                                           76-6004064
        (State of Incorporation,                              (I.R.S. Employer
            or Organization)                                 Identification No.)
          CHASE BANK OF TEXAS,
          NATIONAL ASSOCIATION
        CORPORATE TRUST DIVISION
            712 MAIN STREET
             HOUSTON, TEXAS                                         77002
         (Address of Principal                                   (Zip Code)
           Executive Offices)

       Registrant's Telephone Number, Including Area Code: (713) 216-5712

     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports) and (2) has been subject to such
filing requirements for the past 90 days.  Yes [X]  No [ ]

     Indicate the number of shares outstanding of each of the registrant's
classes of common stock, as of the latest practicable date.

     As of May 8, 1998 -- 4,751,510 Units of Beneficial Interest in TEL Offshore
Trust.

================================================================================
<PAGE>
                   NOTE REGARDING FORWARD-LOOKING STATEMENTS

     This Form 10-Q includes "forward-looking statements" within the meaning
of Section 27A of the Securities Act of 1933, as amended, and Section 21E of the
Securities Exchange Act of 1934, as amended. All statements other than
statements of historical facts included in this Form 10-Q are forward-looking
statements. Although the Working Interest Owners have advised the Trust that
they believe that the expectations reflected in the forward-looking statements
contained herein are reasonable, no assurance can be given that such
expectations will prove to have been correct. Important factors that could cause
actual results to differ materially from expectations ("Cautionary
Statements") are disclosed in this Form 10-Q, including without limitation in
conjunction with the forward-looking statements included in this Form 10-Q. All
subsequent written and oral forward-looking statements attributable to the Trust
or persons acting on its behalf are expressly qualified in their entirety by the
Cautionary Statements.

                                       i
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                        PART I -- FINANCIAL INFORMATION

ITEM 1 -- FINANCIAL STATEMENTS

               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS

                                        MARCH 31,       DECEMBER 31,
                                           1998             1997
                                        ----------      ------------
                                        (UNAUDITED)
ASSETS
Cash and cash equivalents............   $3,330,413       $3,425,376
Net overriding royalty interest in
  producing oil and gas properties,
  net of accumulated amortization of
  $27,628,119 and
  $27,564,441, respectively..........      639,536          703,214
                                        ----------      ------------
Total assets.........................   $3,969,949       $4,128,590
                                        ==========      ============
LIABILITIES AND TRUST CORPUS
Distribution payable to Unit
  holders............................   $1,964,378       $1,952,687
Reserve for future Trust expenses....    1,366,035        1,472,689
Commitments and contingencies (Note
  7).................................
Trust corpus (4,751,510 Units of
  beneficial interest authorized and
  outstanding).......................      639,536          703,214
                                        ----------      ------------
Total liabilities and Trust corpus...   $3,969,949       $4,128,590
                                        ==========      ============

                               TEL OFFSHORE TRUST
                       STATEMENTS OF DISTRIBUTABLE INCOME
                                  (UNAUDITED)

                                           THREE MONTHS ENDED
                                               MARCH 31,
                                       --------------------------
                                           1998          1997
                                       ------------  ------------
Royalty income.......................  $  1,934,392  $  1,126,005
Interest income......................        18,702        10,730
                                       ------------  ------------
                                          1,953,094     1,136,735
Decrease (increase) in reserve for
  future Trust expenses..............       106,654      (297,743)
General and administrative
  expenses...........................       (95,370)     (102,257)
                                       ------------  ------------
Distributable income.................  $  1,964,378  $    736,735
                                       ============  ============
Distributions per Unit (4,751,510
  Units).............................  $    .413421  $    .155052
                                       ============  ============

   The accompanying notes are an integral part of these financial statements.

                                       1
<PAGE>
                               TEL OFFSHORE TRUST
                     STATEMENTS OF CHANGES IN TRUST CORPUS
                                  (UNAUDITED)

                                           THREE MONTHS ENDED
                                               MARCH 31,
                                       --------------------------
                                           1998          1997
                                       ------------  ------------
Trust corpus, beginning of period....  $    703,214  $    938,589
Distributable income.................     1,964,378       736,735
Distribution payable to Unit
  holders............................    (1,964,378)     (736,735)
Amortization of net overriding
  royalty interest...................       (63,678)      (27,585)
                                       ------------  ------------
Trust corpus, end of period..........  $    639,536  $    911,004
                                       ============  ============

   The accompanying notes are an integral part of these financial statements.

                                       2
<PAGE>
                               TEL OFFSHORE TRUST
                         NOTES TO FINANCIAL STATEMENTS
                                  (UNAUDITED)

NOTE 1 -- TRUST ORGANIZATION

     Tenneco Offshore Company, Inc. ("Tenneco Offshore") created the TEL
Offshore Trust ("Trust") effective January 1, 1983, pursuant to the Plan of
Dissolution ("Plan") approved by Tenneco Offshore's stockholders on December
22, 1982. In accordance with the Plan, the TEL Offshore Trust Partnership
("Partnership") was formed in which the Trust owns a 99.99% interest and
Tenneco Oil Company ("Tenneco") initially owned a .01% interest. In general,
the Plan was effected by transferring an overriding royalty interest
("Royalty") equivalent to a 25% net profits interest in the oil and gas
properties (the "Royalty Properties") of Tenneco Exploration, Ltd.
("Exploration I") located offshore Louisiana to the Partnership and issuing
certificates evidencing units of beneficial interest in the Trust ("Units") in
liquidation and cancellation of Tenneco Offshore's common stock.

     On October 31, 1986, Exploration I was dissolved and the oil and gas
properties of Exploration I were distributed to Tenneco subject to the Royalty.
Tenneco, who was then serving as the Managing General Partner of the
Partnership, assumed the obligations of Exploration I, including its obligations
under the instrument conveying the Royalty to the Partnership (the
"Conveyance"). The dissolution of Exploration I had no impact on future cash
distributions to Unit holders.

     On November 18, 1988, Chevron U.S.A. Inc. ("Chevron") acquired most of
the Gulf of Mexico offshore oil and gas properties of Tenneco, including all the
Royalty Properties. As a result of the acquisition, Chevron replaced Tenneco as
the Working Interest Owner and Managing General Partner of the Partnership.
Chevron also assumed Tenneco's obligations under the Conveyance.

     On October 30, 1992, Pennzoil Company ("Pennzoil") acquired certain oil
and gas producing properties from Chevron, including four of the Royalty
Properties. The four Royalty Properties acquired by Pennzoil were East Cameron
354, Eugene Island 348, Eugene Island 367 and Eugene Island 208. As a result of
such acquisition, Pennzoil replaced Chevron as the Working Interest Owner of
such properties on October 30, 1992. Pennzoil also assumed Chevron's obligations
under the Conveyance with respect to such properties.

     On December 1, 1994, Texaco Exploration and Production Inc. ("Texaco")
acquired one of the Royalty Properties from Chevron. The Royalty Property
acquired by Texaco was West Cameron 643. As a result of such acquisition, Texaco
replaced Chevron as the Working Interest Owner of such property on December 1,
1994. Texaco also assumed Chevron's obligations under the Conveyance with
respect to such property.

     On October 1, 1995, SONAT Exploration Company ("SONAT") acquired the East
Cameron 354 property from Pennzoil. In addition, on October 1, 1995, Amoco
Production Company ("Amoco") acquired the Eugene Island 367 property from
Pennzoil. As a result of such acquisitions, SONAT and Amoco have replaced
Pennzoil as the Working Interest Owners of the East Cameron 354 and Eugene
Island 367 properties, respectively, on October 1, 1995 and also assumed
Pennzoil's obligations under the Conveyance with respect to such properties.

     Effective January 1, 1998 Energy Resource Technology, Inc. ("Energy")
acquired the East Cameron 354 property from SONAT. As a result of such
acquisition, Energy replaced SONAT as the Working Interest Owner of the East
Cameron 354 property effective January 1, 1998, and also assumed SONAT's
obligations under the Conveyance with respect to such property.

     All of the Royalty Properties continue to be subject to the Royalty, and it
is anticipated that the Trust and the Partnership, in general, will continue to
operate as if the above-described sales of the Royalty Properties had not
occurred.

                                       3
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

     Unless the context in which such terms are used indicates otherwise, in
these Notes the terms "Working Interest Owner" and "Working Interest Owners"
generally refer to the owner or owners of the Royalty Properties (Exploration I
through October 31, 1986; Tenneco for periods from October 31, 1986 until
November 18, 1988; Chevron with respect to all Royalty Properties for periods
from November 18, 1988 until October 30, 1992, and with respect to all Royalty
Properties except East Cameron 354, Eugene Island 348, Eugene Island 367 and
Eugene Island 208 for periods from October 30, 1992 until December 1, 1994, and
with respect to the same properties except West Cameron 643 thereafter; Pennzoil
with respect to East Cameron 354, Eugene Island 348, Eugene Island 367 and
Eugene Island 208 for periods from October 30, 1992 until October 1, 1995, and
with respect to Eugene Island 348 and Eugene Island 208 thereafter; Texaco with
respect to West Cameron 643 for periods beginning on or after December 1, 1994;
SONAT with respect to East Cameron 354 for periods beginning on or after October
1, 1995; and Amoco with respect to Eugene Island 367 for periods beginning on or
after October 1, 1995; and Energy with respect to East Cameron 354 for periods
beginning on or after January 1, 1998).

NOTE 2 -- BASIS OF ACCOUNTING

     The accompanying unaudited financial information has been prepared by Chase
Bank of Texas, National Association ("Corporate Trustee") in accordance with
the instructions to Form 10-Q and does not include all of the information
required by generally accepted accounting principles for complete financial
statements, although the Corporate Trustee and the individual trustees
(collectively, the "Trustees") believe that the disclosures are adequate to
make the information presented not misleading. The information furnished
reflects all adjustments which are, in the opinion of the Trustees, necessary
for a fair presentation of the results for the interim periods presented. The
financial information should be read in conjunction with the financial
statements and notes thereto included in the Trust's Annual Report on Form 10-K
for the year ended December 31, 1997.

     The financial statements of the Trust are prepared on the following basis:

          (a)  Royalty income is recorded when received by the Corporate Trustee
               on the last business day of each calendar quarter; and

          (b)  Trust general and administrative expenses are recorded when paid,
               except for the cash reserved for future general and
               administrative expenses, as discussed in Note 6.

     This manner of reporting income and expenses is considered to be the most
meaningful because the quarterly distributions to Unit holders are based on net
cash receipts received from the Working Interest Owners. The financial
statements of the Trust differ from financial statements prepared in accordance
with generally accepted accounting principles, because, under such principles,
Royalty income and Trust general and administrative expenses for a quarter would
be recognized on an accrual basis. In addition, amortization of the overriding
royalty interest, which is calculated on a units-of-production basis, is charged
directly to Trust corpus since such amount does not affect distributable income.

     Cash and cash equivalents include all highly liquid short term investments
with original maturities of three months or less.

NOTE 3 -- OVERRIDING ROYALTY INTEREST

     The Royalty entitles the Trust to its share (99.99%) of 25% of the Net
Proceeds attributable to the Royalty Properties. The Conveyance, dated January
1, 1983, provides that the Working Interest Owners will calculate, for each
period of three months commencing the first day of February, May, August and
November, an amount equal to 25% of the Net Proceeds from their oil and gas
properties for the period.

                                       4
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

Generally, Net Proceeds are the amounts received by the Working Interest Owners
from the sale of minerals from the Royalty Properties less operating and capital
costs incurred, management fees and expense reimbursements owing the Managing
General Partner of the Partnership, applicable taxes other than income taxes,
and cash escrows. Cash escrows are for the future costs to be incurred to plug
and abandon wells, dismantle and remove platforms, pipelines and other
production facilities, and for the estimated amount of future capital
expenditures on the Royalty Properties. Net Proceeds do not include amounts
received by the Working Interest Owners as advance gas payments, "take-or-pay"
payments or similar payments unless and until such payments are extinguished or
repaid through the future delivery of gas.

NOTE 4 -- DISTRIBUTIONS TO UNIT HOLDERS

     In accordance with the provisions of the Trust Agreement, generally all Net
Proceeds received by the Trust, net of Trust general and administrative expenses
and any cash reserves established for the payment of contingent or future
obligations of the Trust, are distributed currently to the Unit holders. The
amounts distributed are determined on a quarterly basis and are payable to Unit
holders of record as of the last business day of each calendar quarter. However,
cash distributions are made in January, April, July and October and include
interest earned from the quarterly record date to the date of distribution.

NOTE 5 -- SPECIAL COST ESCROW ACCOUNT

     The Conveyance provides for reserving funds for estimated future "Special
Costs" of plugging and abandoning wells, dismantling platforms and other costs
of abandoning the Royalty Properties, as well as for the estimated amount of
future drilling projects and other capital expenditures on the Royal Properties.
As provided in the Conveyance, the amount of funds to be reserved is determined
based on factors including estimates of aggregate future production costs,
aggregate future Special Costs, aggregate future net revenues and actual current
net proceeds. Deposits into this account reduce current distributions and are
placed in an escrow account and invested in short-term certificates of deposit.
Such account is herein referred to as the "Special Cost Escrow Account." The
Trust's share of interest generated from the Special Cost Escrow Account serves
to reduce the Trust's share of allocated production costs. Special Cost Escrow
funds will generally be utilized to pay Special Costs to the extent there are
not adequate current net proceeds to pay such costs. Special Costs that have
been paid are no longer included in the Special Cost Escrow calculation.
Deposits to the Special Cost Escrow Account will generally be made when the
balance in the Special Cost Escrow Account is less than 125% of future Special
Costs and there is a Net Revenues Shortfall (a calculation of the excess of
estimated future costs over estimated future net revenues pursuant to a formula
contained in the Conveyance). When there is not a Net Revenues Shortfall,
amounts in the Special Cost Escrow Account will generally be released, to the
extent that Special Costs have been incurred. Amounts in the Special Cost Escrow
Account generally will also be released when the balance in such account exceeds
125% of future Special Costs. In the first quarter of 1997, there was a net
deposit of funds into the Special Cost Escrow Account. The Trust's share of the
funds deposited was approximately $344,000. The deposit was primarily a result
of an increase in the current estimate of projected capital expenditures,
production costs and abandonment costs of the Royalty Properties. In the first
quarter of 1998, there was a net release of funds from the Special Cost Escrow
Account. The Trust's share of the funds released was approximately $513,800. The
release was primarily a result of a decrease in the current estimate of
projected capital expenditures of the Royalty Properties. As of March 31, 1998,
approximately $4,108,000 remained in the Special Cost Escrow Account.

     Chevron, in its capacity as Managing General Partner, has advised the Trust
that additional deposits to the Special Cost Escrow Account may be required in
future periods in connection with other production

                                       5
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

costs, other abandonment costs, other capital expenditures and changes in the
estimates and factors described above. Such deposits could result in a
significant reduction in Royalty income in the periods in which such deposits
are made, including the possibility that no Royalty income would be received in
such periods.

NOTE 6 -- EXPENSE RESERVE

     At December 31, 1991, a cash reserve of $120,000 had been established for
future Trust general and administrative expenses. During 1992 and 1993, in
anticipation of future periods when the cash received from the Royalty may not
be sufficient for payment of Trust expenses, the reserve for future Trust
general and administrative expenses was increased each quarter by an amount
equal to the difference between $150,000 and the amount of the Trust's general
and administrative expenses for such quarter. In March 1994, the Trust
determined, in accordance with the Trust Agreement, to begin further increasing
the Trust's cash reserve each quarter by an amount equal to the difference
between $200,000 and the amount of the Trust's general and administrative
expenses for such quarter. During 1996, the Trust used $397,845 from the Trust's
cash reserve account to pay the Trust's general and administrative expenses for
the first, second and fourth quarters, when no royalty income was received by
the Trust. In the third quarter of 1996, when Royalty income was received, the
Trust reserved $99,536. Therefore, the net cash used from the Trust's cash
reserve account in 1996 was $298,309. During 1997, the aggregate amount of cash
reserved by the Trust was $593,066. In the first quarter of 1998, the Trust
determined that the Trust's cash reserve was currently sufficient to provide for
future administrative expenses in connection with the winding up of the Trust.
The Trust determined that a cash reserve equal to three times the average
expenses of the Trust during each of the past three fiscal years was sufficient
at this time to provide for future administrative expenses in connection with
the winding up of the Trust. This reserve amount for 1998 is $1,366,035. The
excess amount of $106,654 was distributed to Unit holders in the first quarter
of 1998, and no deposits are expected to be made to the Trust's cash reserve
account during 1998.

NOTE 7 -- COMMITMENTS AND CONTINGENCIES

     During 1994, Pennzoil, the Working Interest Owner on the Eugene Island 348
property, settled a gas imbalance on that property for approximately $2,696,000.
The Trust's share of this settlement amount was approximately $674,000, of which
approximately $359,500 has been recovered from the Trust by the Working Interest
Owner through the first quarter of 1998, and the remainder will be subject to
recovery from the Trust in future periods, in accordance with the Conveyance.
The Working Interest Owner has advised the Trust that future Royalty income
attributable to all of the Royalty Properties owned by Pennzoil will be used to
offset the Trust's share of such settlement amounts. Based on current
production, prices and expenses for the Royalty Properties owned by Pennzoil, it
is estimated that Royalty income attributable to such properties will be
retained by Pennzoil for the remaining life of the Trust. The Trust does not
anticipate that retention of such Royalty income by Pennzoil will have a
material effect on the Trust's Royalty income as a whole.

     The Working Interest Owners have advised the Trust that, although they
believe that they are in general compliance with applicable health, safety and
environmental laws and regulations that have taken effect at the federal, state
and local levels, costs may be incurred to comply with current and proposed
environmental legislation which could result in increased operating expenses on
the Royalty Properties.

                                       6
<PAGE>
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS

FINANCIAL REVIEW

THREE MONTHS ENDED MARCH 31, 1998 AND 1997

     Distributions to Unit holders for the three months ended March 31, 1998
amounted to $1,964,378 or $.413421 per Unit as compared to $736,735 or $.155052
per Unit for the same period in 1997. The increase in distributable income for
the first quarter of 1998 was primarily due to a net release of $513,800 from
the Trust's Special Cost Escrow Account as compared to a net deposit of $344,000
in the first quarter of 1997 and a release of $106,654 from the Trust's cash
reserve account.

     Gas revenues decreased approximately 46% in the first quarter of 1998
compared to the first quarter of 1997 primarily due to a 30% decrease in gas
volumes. This decrease was primarily attributable to the B-15 well watering out
on the Ship Shoal 182/183 property in the first quarter of 1998. In addition,
there was a 21% decrease in the average price received for natural gas from
$3.50 per Mcf in the first quarter of 1997 to $2.75 per Mcf in the first quarter
of 1998. Crude oil and condensate revenues decreased approximately 21% in the
first quarter of 1998 in comparison to the same period in 1997 primarily due to
a 26% decrease in the average price received from $23.37 per barrel in the first
quarter of 1997 to $17.24 per barrel in the first quarter of 1998. The decrease
in price was slightly offset by an 8% increase in crude oil and condensate
volumes from the 1997 first quarter to the 1998 first quarter. The Trust's share
of capital expenditures increased approximately 17% or $116,792 in the first
quarter of 1998 as compared to the same period in 1997 primarily due to drilling
activity on the B-7, B-9 and B-12 wells on the Eugene Island 339 property in the
first quarter of 1998. The Trust's share of operating expenses decreased by
approximately 76% or $356,808 in the first quarter of 1998 as compared to the
same period in 1997 due primarily to a workover on the E-9 well on the Ship
Shoal 182/183 property in the first quarter of 1997 and the removal of a
compressor from the West Cameron 643 property in the first quarter of 1998.

     For the first quarter of 1998, the Trust had undistributed net income of
$32,465. Undistributed net income represents positive Net Proceeds generated
during the period that were applied to an existing loss carryforward. The
undistributed net income for the first quarter of 1998 was primarily related to
the Eugene Island 348 gas imbalance settlement in 1994. See Note 7 in the Notes
to Financial Statements for information regarding such settlement.

     In the first quarter of 1998, there was a net release of funds from the
Special Cost Escrow Account. The Trust's share of the funds released was
approximately $513,800, compared to a deposit of funds into the Special Cost
Escrow Account of $344,000 net to the Trust in the first quarter of 1997. The
Special Cost Escrow is set aside for estimated abandonment costs and future
capital expenditures as provided for in the Conveyance. For additional
information relating to the Special Cost Escrow see "Special Cost Escrow
Account" below.

RESERVE FOR FUTURE TRUST EXPENSES

     In accordance with the provisions of the Trust Agreement, generally all Net
Proceeds received by the Trust, net of Trust general and administrative expenses
and any cash reserves established for the payment of contingent or future
obligations of the Trust, are distributed currently to the Unit holders. During
1992 and 1993, in anticipation of future periods when the cash received from the
Royalty may not be sufficient for payment of Trust expenses, the reserve for
future Trust general and administrative expenses was increased each quarter by
an amount equal to the difference between $150,000 and the amount of the Trust's
general and administrative expenses for such quarter. In March 1994, the Trust
determined, in accordance with the Trust Agreement, to begin further increasing
the Trust's cash reserve each quarter by an amount equal to the

                                       7
<PAGE>
difference between $200,000 and the amount of the Trust's general and
administrative expenses for such quarter. During 1996, the Trust used cash of
$397,845 from the Trust's cash reserve account to pay the Trust's general and
administrative expenses due to the absence of Royalty income during the first,
second and fourth quarters. In the third quarter of 1996, when Royalty income
was received, the Trust reserved $99,536. Therefore, the net cash used from the
Trust's cash reserve account in 1996 was $298,309. During 1997, the aggregate
amount of cash reserved by the Trust was $593,066. The total amount of the
Trust's cash reserve at December 31, 1997 was $1,472,689. In addition, in the
first quarter of 1998, the Trust has determined that the Trust's cash reserve is
currently sufficient to provide for future administrative expenses in connection
with the winding up of the Trust. The Trust has determined that a cash reserve
equal to three times the average expenses of the Trust during each of the past
three fiscal years is sufficient at this time to provide for future
administrative expenses in connection with the winding up of the Trust. This
reserve amount for 1998 is $1,366,035. The excess amount of $106,654 was
distributed to Unit holders in the first quarter of 1998, and no deposits are
expected to be made to the Trust's cash reserve account during 1998.

OTHER

     The amount of cash distributed by the Trust is dependent on, among other
things, the sales prices and quantities of oil and gas produced from the Royalty
Properties. It should be noted that substantial uncertainties exist with regard
to future oil and gas prices, which are subject to material fluctuations due to
changes in production levels and pricing and other actions taken by major
petroleum producing nations, as well as the regional supply and demand for oil
and gas, weather, industrial growth, conservation measures, competition and
other variables.

OPERATIONAL REVIEW

THREE MONTHS ENDED MARCH 31, 1998 AND 1997

     VOLUMES AND DOLLAR AMOUNTS DISCUSSED BELOW REPRESENT AMOUNTS RECORDED BY
THE WORKING INTEREST OWNERS UNLESS OTHERWISE SPECIFIED.

     Ship Shoal 182/183 crude oil revenues decreased from $5,672,614 in the
first quarter of 1997 to $4,628,394 in the first quarter of 1998, primarily due
to a decrease in the average crude oil price from $23.81 per barrel in the first
quarter of 1997 to $17.67 per barrel for the same period in 1998. The decrease
in price was slightly offset by an increase in crude oil production from 238,290
barrels in the first quarter of 1997 to 261,918 barrels in the first quarter of
1998. The increase in crude oil production was due primarily to the high
production levels on the B-11, B-12 and B-13 wells which were drilled in 1996.
Gas revenues decreased from $1,350,658 in the first quarter of 1997 to $883,244
in the first quarter of 1998 primarily due to a decrease in gas volumes from
377,503 Mcf in the first quarter of 1997 to 330,190 Mcf in the first quarter of
1998. The decrease in gas volumes was primarily due to the B-15 well watering
out in the first quarter of 1998. In addition, there was a decrease in the
average natural gas sales price from $3.64 per Mcf in the first quarter of 1997
to $2.82 per Mcf in the same period of 1998. The majority of the gas from this
property is currently being purchased by NGC Corporation ("NGC") at a
calculated price based on the monthly FERC Tennessee-Louisiana Zone 1 index. In
addition, the Working Interest Owner has advised the Trust that approximately
59,716 Mcf have been overtaken by the Working Interest Owner from this property
as of January 31, 1998. The Trust's share of this overtake position is
approximately 14,929 Mcf. Accordingly, gas revenues from this property may be
reduced in future periods while underproduced parties recover their share of the
gas imbalance. Chevron has advised the Trust that sufficient gas reserves exist
on Ship Shoal 182/183 for underproduced parties to recoup their share of the gas
imbalance on this property. Capital expenditures decreased from $2,252,664 in
the first quarter of 1997 to $196,876 for the same period in 1998 due to the
drilling and completing of the B-11, B-12 and B-13 wells in the first three
quarters of 1996. Operating expenses decreased from $742,604 in the first
quarter of 1997 to $425,308 for the same

                                       8
<PAGE>
period in 1998 due to the workover on the E-9 well in the first quarter of 1997.
The Working Interest Owner has advised the Trust that it plans to drill a
delineation well on this property in late 1998 at an approximate cost of $2.5
million ($625,000 net to the Trust).

     Eugene Island 339 crude oil revenues decreased from $1,723,866 in the first
quarter of 1997 to $1,161,849 in the first quarter of 1998 due primarily to a
decrease in the average crude oil price from $22.03 per barrel in the first
quarter of 1997 to $15.68 per barrel in the first quarter of 1998. In addition,
there was a decrease in volumes from 78,257 barrels in the first quarter of 1997
to 74,103 barrels in the first quarter of 1998. Gas revenues decreased from
$376,421 in the first quarter of 1997 to $296,844 in the first quarter of 1998
due to a decrease in the average price received for natural gas from $3.50 per
Mcf in the first quarter of 1997 to $2.84 per Mcf for the same period in 1998.
In addition, there was a decrease in gas volumes from 112,700 Mcf in the first
quarter of 1997 to 110,702 Mcf in the first quarter of 1998. The Working
Interest Owner has advised the Trust that there is an overtake imbalance
position of approximately 23,454 Mcf on this property as of January 31, 1998.
The Trust's share of this overtake position is approximately 5,864 Mcf.
Accordingly, gas revenues from this property may be reduced in future periods
while underproduced parties recoup their share of the gas imbalance. Chevron has
advised the Trust that sufficient gas reserves exist on the Eugene Island 339
for underproduced parties to recoup their share of the gas imbalance on this
property. The gas from this property is currently committed to NGC pursuant to
an agreement providing for gas to be purchased at a calculated price based on
the monthly Inside FERC Tennessee-Louisiana Zone 1 index. Capital expenditures
increased $1,454,387 from first quarter 1997 to first quarter 1998 due primarily
to drilling activity on the B-7, B-9 and B-12 wells in the first quarter of
1998. Operating expenses decreased from $440,847 in the first quarter of 1997 to
$138,407 for the same period in 1998 due to an adjustment to properly reflect
capital costs in the first quarter of 1998. The Working Interest Owner has
advised the Trust that it plans to drill the B-4 and B-16 sidetrack wells in
early 1998 at an aggregate cost of approximately $2.2 million ($550,000 net to
the Trust).

     West Cameron 643 gas revenues decreased from $4,580,602 in the first
quarter of 1997 to $1,990,085 in the first quarter of 1998 due primarily to a
decrease in gas volumes from 1,311,126 Mcf in the first quarter of 1997 to
738,177 Mcf for the same period in 1998. The decrease in gas volumes was due
primarily to the B-8 well being taken off of production in December 1997. In
addition, there was a decrease in the average price received for natural gas
from $3.49 per Mcf in the first quarter of 1997 to $2.70 per Mcf in the first
quarter of 1998. The Working Interest Owner has advised the Trust that the gas
from this property is currently committed under the contract with Texaco Natural
Gas, Inc. pursuant to an agreement for gas to be purchased at a price based on
the monthly Inside FERC Tennessee-Louisiana Zone 1 index. Capital expenditures
decreased from $399,395 in the first quarter of 1997 to $158,090 in the first
quarter of 1998 due primarily to costs paid in first quarter of 1997 which were
associated with workovers on the A-2, A-6, A-9, A-10, A-16 and B-3 wells in
1996. Operating expenses decreased $661,480 in the first quarter of 1998 from
the same period in 1997 due primarily to lower costs as a result of the removal
of a compressor from the property in the first quarter of 1998.

     In May 1998, Chevron advised the Trust that production began in May, 1998
on the two wells on the East Cameron 371 property. The Trust has been advised by
the Working Interest Owner on this property that the well is currently producing
approximately 30,600 Mcf of gas per day.

FUTURE NET REVENUES AND TERMINATION OF THE TRUST

     Based on a reserve study provided to the Trust by DeGolyer and MacNaughton,
independent petroleum engineers, it was estimated that as of October 31, 1997
future net revenues attributable to the Trust's royalty interests approximated
$24.3 million. Such reserve study also indicates that approximately 80% of the
future net revenues from the Royalty Properties are expected to be received by
the Trust during the next 3 years. In addition, because the Trust will terminate
in the event estimated future net revenues fall below

                                       9
<PAGE>
$2 million, it would be possible for the Trust to terminate even though some or
all of the Royalty Properties continued to have remaining productive lives. Upon
termination of the Trust, the Trustees will sell for cash all of the assets held
in the Trust estate and make a final distribution to Unit holders of any funds
remaining after all Trust liabilities have been satisfied. The estimates of
future net revenues discussed above are subject to large variances from year to
year and should not be construed as exact. There are numerous uncertainties
present in estimating future net revenues for the Royalty Properties. The
estimate may vary depending on changes in market prices for crude oil and
natural gas, the recoverable reserves, annual production and costs assumed by
DeGolyer and MacNaughton. In addition, future economic and operating conditions
as well as results of future drilling plans may cause significant changes in
such estimate. The discussion set forth above is qualified in its entirety by
reference to the Trust's 1997 Annual Report on Form 10-K. The Form 10-K is
available upon request from the Corporate Trustee.

SPECIAL COST ESCROW ACCOUNT

     The Conveyance provides for reserving funds for estimated future "Special
Costs" of plugging and abandoning wells, dismantling platforms and other costs
of abandoning the Royalty Properties, as well as for the estimated amount of
future drilling projects and other capital expenditures on the Royalty
Properties. As provided in the Conveyance, the amount of funds to be reserved is
determined based on factors including estimates of aggregate future production
costs, aggregate future Special Costs, aggregate future net revenues and actual
current net proceeds. Deposits into this account reduce current distributions
and are placed in an escrow account and invested in short-term certificates of
deposit. Such account is herein referred to as the "Special Cost Escrow
Account." The Trust's share of interest generated from the Special Cost Escrow
Account serves to reduce the Trust's share of allocated production costs.
Special Cost Escrow funds will generally be utilized to pay Special Costs to the
extent there are not adequate current net proceeds to pay such costs. Special
Costs that have been paid are no longer included in the Special Cost Escrow
calculation. Deposits to the Special Cost Escrow Account will generally be made
when the balance in the Special Cost Escrow Account is less than 125% of future
Special Costs and there is a Net Revenues Shortfall (a calculation of the excess
of estimated future costs over estimated future net revenues pursuant to a
formula contained in the Conveyance). When there is not a Net Revenues
Shortfall, amounts in the Special Cost Escrow Account will generally be
released, to the extent that Special Costs have been incurred. Amounts in the
Special Cost Escrow Account generally will also be released when the balance in
such account exceeds 125% of future Special Costs. In the first quarter of 1997,
there was a net deposit of funds into the Special Cost Escrow Account. The
Trust's share of the funds deposited was approximately $344,000. The deposit was
primarily a result of an increase in the current estimates of projected capital
expenditures, production costs and abandonment costs of the Royalty Properties.
In the first quarter of 1998, there was a net release of funds from the Special
Cost Escrow Account. The Trust's share of the funds released was approximately
$513,800. The release was primarily a result of a decrease in the current
estimate of projected capital expenditures of the Royalty Properties. As of
March 31, 1998, approximately $4,108,000 remained in the Special Cost Escrow
Account.

     Chevron, in its capacity as Managing General Partner, has advised the Trust
that additional deposits to the Special Cost Escrow Account may be required in
future periods in connection with other production costs, other abandonment
costs, other capital expenditures and changes in the estimates and factors
described above. Such deposits, if made, could result in a significant reduction
in Royalty income in the periods in which such deposits are made, including the
possibility that no Royalty income would be received in such periods.

                                       10
<PAGE>
OVERVIEW OF PRODUCTION, PRICES AND NET PROCEEDS

     The following schedule provides a summary of the volumes and weighted
average prices for crude oil and condensate and natural gas recorded by the
Working Interest Owners for the Royalty Properties, as well as the Working
Interest Owners' calculations of the net proceeds and the royalties paid to the
Trust during the periods indicated. Net proceeds due to the Trust are calculated
for each three month period commencing on the first day of February, May, August
and November.

                                                   ROYALTY PROPERTIES       
                                                   THREE MONTHS ENDED
                                                      MARCH 31,(1)
                                             ------------------------------
                                                  1998            1997
                                             --------------  --------------
Crude oil and condensate (bbls).........            342,275         318,084
Natural gas and gas products (Mcf)......          1,355,007       1,948,682
Crude oil and condensate average price,    
  per bbl...............................     $        17.24  $        23.37
Natural gas average price, per Mcf         
  (excluding gas products)..............     $         2.75  $         3.50
Crude oil and condensate revenues.......     $    5,902,006  $    7,432,984
Natural gas and gas products revenues...          3,670,052       6,775,531
Production expenses.....................           (597,180)     (2,255,824)
Capital expenditures....................         (3,161,966)     (2,694,799)
Undistributed Net Loss (Income)(2)......           (129,859)     (3,377,496)
(Provision for) Refund of escrowed         
  special costs.........................          2,055,287      (1,375,924)
                                             --------------  --------------
NET PROCEEDS............................          7,738,340       4,504,472
Royalty interest........................               x25%            x25%
                                             --------------  --------------
Partnership share.......................          1,934,585       1,126,118
Trust interest..........................            x99.99%         x99.99%
                                             --------------  --------------
Trust share.............................     $    1,934,392  $    1,126,005
                                             ==============  ==============
                                        
------------

(1) The amounts for the three months ended March 31, 1998 and 1997 represent
    actual production for the periods November 1997 through January 1998 and
    November 1996 through January 1997, respectively.

(2) Undistributed net loss represents negative Net Proceeds generated during the
    respective period. An undistributed net loss is carried forward and offset,
    in future periods, by positive Net Proceeds earned by the related Working
    Interest Owner(s). Undistributed net income represents positive Net
    Proceeds, generated during the respective period, that were applied to an
    existing loss carryforward. As of March 31, 1998, the loss carryforward was
    $1,554,600 ($388,650 net to the Trust).

                                       11
<PAGE>
                          PART II -- OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.

(A)  EXHIBITS

     (Asterisk indicates exhibit previously filed with the Securities and
Exchange Commission and incorporated herein by reference.)
<TABLE>
<CAPTION>
                                                                                  SEC FILE OR
                                                                                 REGISTRATION      EXHIBIT
                                                                                    NUMBER         NUMBER
                                                                                 -------------     -------
<S>           <C>                                                                <C>               <C>
4(a)*     --  Trust Agreement dated as of January 1, 1983, among Tenneco
              Offshore Company, Inc., Texas Commerce Bank National
              Association, as corporate trustee, and Horace C. Bailey, Joseph
              C. Broadus and F. Arnold Daum, as individual trustees (Exhibit
              4(a) to Form 10-K for the year ended December 31, 1992 of TEL
              Offshore Trust)................................................        0-6910           4(a)
4(b)*     --  Agreement of General Partnership of TEL Offshore Trust
              Partnership between Tenneco Oil Company and the TEL Offshore
              Trust, dated January 1, 1983 (Exhibit 4(b) to Form 10-K for
              year ended December 31, 1992 of TEL Offshore Trust)............        0-6910           4(b)
4(c)*     --  Conveyance of Overriding Royalty Interests from Exploration I
              to the Partnership (Exhibit 4(c) to Form 10-K for year ended
              December 31, 1992 of TEL Offshore Trust).......................        0-6910           4(c)
4(d)*     --  Amendments to TEL Offshore Trust Trust Agreement, dated
              December 7, 1984 (Exhibit 4(d) to Form 10-K for year ended
              December 31, 1992 of TEL Offshore Trust).......................        0-6910           4(d)
4(e)*     --  Amendment to the Agreement of General Partnership of TEL
              Offshore Trust Partnership, effective as of January 1, 1983
              (Exhibit 4(e) to Form 10-K for year ended December 31, 1992 of
              TEL Offshore Trust)............................................        0-6910           4(e)
10(a)*    --  Purchase Agreement, dated as of December 7, 1984 by and between
              Tenneco Oil Company and Tenneco Offshore II Company (Exhibit
              10(a) to Form 10-K for year ended December 31, 1992, of TEL
              Offshore Trust)................................................        0-6910          10(a)
10(b)*    --  Consent Agreement, dated November 16, 1988, between TEL
              Offshore Trust and Tenneco Oil Company (Exhibit 10(b) to Form
              10-K for year ended December 31, 1988 of TEL Offshore Trust)...        0-6910          10(b)
10(c)*    --  Assignment and Assumption Agreement, dated November 17, 1988,
              between Tenneco Oil Company and TOC-Gulf of Mexico Inc.
              (Exhibit 10(c) to Form 10-K for year ended December 31, 1988 of
              TEL Offshore Trust)............................................        0-6910          10(c)
10(d)*    --  Gas Purchase and Sales Agreement Effective September 1, 1993
              between Tennessee Gas Pipeline Company and Chevron U.S.A.
              Production Company (Exhibit 10(d) to Form 10-K for year ended
              December 31, 1993 of TEL Offshore Trust).......................        0-6910          10(d)
27(a)     --  Financial Data Schedule
</TABLE>
(B)  REPORTS ON FORM 8-K

     No reports on Form 8-K were filed with the Securities and Exchange
Commission during the first quarter of 1998.

                                       12
<PAGE>
                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                                          TEL OFFSHORE TRUST
                                          By:  Chase Bank of Texas, National
                                               Association, Corporate Trustee
                                          By:  /s/   PETE FOSTER
                                                     PETE FOSTER
                                                SENIOR VICE PRESIDENT
                                                   AND TRUST OFFICER

Date: May 11, 1998

The Registrant, TEL Offshore Trust, has no principal executive officer,
principal financial officer, board of directors or persons performing similar
functions. Accordingly, no additional signatures are available and none have
been provided.

                                       13