<PAGE>   1
================================================================================

                       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

                                       OR

              [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15 (d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

             FOR THE QUARTER ENDED MARCH 31, 1999


                           COMMISSION FILE NO. 1-13603
                TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

            DELAWARE                                          76-0329620
     (STATE OF INCORPORATION                               (I.R.S. EMPLOYER
         OR ORGANIZATION)                                IDENTIFICATION NUMBER)


                               2929 ALLEN PARKWAY
                                 P.O. BOX 2521
                           HOUSTON, TEXAS 77252-2521
          (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES, INCLUDING ZIP CODE)

                                 (713) 759-3636
              (REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE)

         Indicate by check mark whether each 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 [ ]

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



<PAGE>   2

                          PART I. FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS

                TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP

                           CONSOLIDATED BALANCE SHEETS
                                 (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                     MARCH 31,     DECEMBER 31,
                                                                       1999           1998
                                                                   ------------   ------------
                                                                   (UNAUDITED)
<S>                                                                <C>            <C>         
                                     ASSETS
Current assets:
  Cash and cash equivalents ....................................   $     27,728   $     36,723
  Short-term investments .......................................          3,271          3,269
  Accounts receivable, trade ...................................         18,686         17,740
  Inventories ..................................................         12,754         13,392
  Other ........................................................          1,478          1,509
                                                                   ------------   ------------
     Total current assets ......................................         63,917         72,633
                                                                   ------------   ------------
Property, plant and equipment, at cost (Net of accumulated
  depreciation and amortization of $198,236 and $192,960) ......        572,484        567,566
Investments ....................................................          4,723          6,490
Intangible assets ..............................................         36,363         36,842
Advances to limited partner ....................................          2,399          1,989
Other assets ...................................................         10,933         10,966
                                                                   ------------   ------------
     Total assets ..............................................   $    690,819   $    696,486
                                                                   ============   ============

                        LIABILITIES AND PARTNERS' CAPITAL

Current liabilities:
  Accounts payable and accrued liabilities .....................   $      5,702   $      8,513
  Accounts payable, general partner ............................          3,338          2,815
  Accrued interest .............................................          6,180         13,039
  Other accrued taxes ..........................................          4,918          5,878
  Other ........................................................          5,252          6,974
                                                                   ------------   ------------
     Total current liabilities .................................         25,390         37,219
                                                                   ------------   ------------
Senior Notes ...................................................        389,730        389,722
Other long-term debt ...........................................         38,000         38,000
Other liabilities and deferred credits .........................          3,139          3,407
Partners' capital:
  General partner's interest ...................................          2,372          2,306
  Limited partner's interest ...................................        232,188        225,832
                                                                   ------------   ------------
     Total partners' capital ...................................        234,560        228,138
                                                                   ------------   ------------
     Total liabilities and partners' capital ...................   $    690,819   $    696,486
                                                                   ============   ============
</TABLE>


          See accompanying Notes to Consolidated Financial Statements.



                                       2
<PAGE>   3

                       TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP

                               CONSOLIDATED STATEMENTS OF INCOME
                                          (UNAUDITED)
                                         (IN THOUSANDS)

<TABLE>
<CAPTION>
                                                                      THREE MONTHS     THREE MONTHS
                                                                         ENDED           ENDED
                                                                       MARCH 31,        MARCH 31,
                                                                         1999             1998
                                                                      ------------    ------------
<S>                                                                   <C>             <C>
Operating revenues:
  Transportation - Refined products .............................     $     25,596    $     22,462
  Transportation - LPGs .........................................           26,595          21,815
  Mont Belvieu operations .......................................            2,897           2,670
  Other -  net ..................................................            6,062           3,258
                                                                      ------------    ------------
     Total operating revenues ...................................           61,150          50,205
                                                                      ------------    ------------

Costs and expenses:
  Operating, general and administrative .........................           17,121          15,844
  Operating fuel and power ......................................            6,559           6,190
  Depreciation and amortization .................................            6,763           6,080
  Taxes - other than income taxes ...............................            2,509           2,577
                                                                      ------------    ------------
     Total costs and expenses ...................................           32,952          30,691
                                                                      ------------    ------------

     Operating income ...........................................           28,198          19,514

Interest expense ................................................           (7,536)         (7,156)
Interest costs capitalized ......................................              142             284
Other income - net ..............................................              402             647
                                                                      ------------    ------------

     Income before extraordinary loss on debt extinguishment.....           21,206          13,289

Extraordinary loss on debt extinguishment .......................             --           (73,509)
                                                                      ------------    ------------

     Net income (loss) ..........................................     $     21,206    $    (60,220)
                                                                      ============    ============
</TABLE>



          See accompanying Notes to Consolidated Financial Statements.




                                       3
<PAGE>   4


                TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP

                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (UNAUDITED)
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                     THREE MONTHS    THREE MONTHS
                                                                        ENDED           ENDED
                                                                       MARCH 31,       MARCH 31,
                                                                         1999           1998
                                                                     ------------    ------------
<S>                                                                  <C>             <C>          
Cash flows from operating activities:
  Net income (loss) ..............................................   $     21,206    $    (60,220)
  Adjustments to reconcile net income (loss) to cash provided by
   operating activities:
     Depreciation and amortization ...............................          6,763           6,080
     Extraordinary loss on early extinguishment of debt ..........           --            73,509
     Equity in loss of affiliate .................................             74              94
     Decrease (increase) in accounts receivable, trade ...........           (946)          6,563
     Decrease (increase) in inventories ..........................            638          (1,080)
     Decrease in other current assets ............................             31             250
     Decrease in accounts payable and accrued expenses ...........        (11,829)        (11,087)
     Other .......................................................           (541)            (63)
                                                                     ------------    ------------
          Net cash provided by operating activities ..............         15,396          14,046
                                                                     ------------    ------------

Cash flows from investing activities:
  Proceeds from investments ......................................          3,000            --
  Purchases of cash investments ..................................         (1,235)           --
  Purchase of fractionators and related intangible assets,
          net of noncash portion .................................           --            (2,000)
  Capital expenditures ...........................................        (11,069)         (4,949)
                                                                     ------------    ------------
          Net cash used in investing activities ..................         (9,304)         (6,949)
                                                                     ------------    ------------

Cash flows from financing activities:
  Principal payment, First Mortgage Notes ........................           --          (326,512)
  Prepayment premium, First Mortgage Notes .......................           --           (70,093)
  Issuance of Senior Notes .......................................           --           389,694
  Debt issuance costs, Senior Notes ..............................           --            (3,641)
  Advances to Limited Partner ....................................           (410)           --
  Distributions ..................................................        (14,677)        (13,710)
                                                                     ------------    ------------
          Net cash used in financing activities ..................        (15,087)        (24,262)
                                                                     ------------    ------------

Net decrease in cash and cash equivalents ........................         (8,995)        (17,165)

Cash and cash equivalents at beginning of period .................         36,723          43,961
                                                                     ------------    ------------
Cash and cash equivalents at end of period .......................   $     27,728    $     26,796
                                                                     ============    ============

SUPPLEMENTAL DISCLOSURE OF CASH FLOWS:
Interest paid during the period (net of capitalized interest) ....   $     14,182    $     12,525
                                                                     ============    ============
</TABLE>



          See accompanying Notes to Consolidated Financial Statements.



                                       4
<PAGE>   5

                TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (UNAUDITED)

NOTE 1.  ORGANIZATION AND BASIS OF PRESENTATION

         TE Products Pipeline Company, Limited Partnership (the "Partnership"),
a Delaware limited partnership, was formed in March 1990. TEPPCO Partners, L.P.
(the "Parent Partnership") owns a 98.9899% interest as the sole limited partner
interest and Texas Eastern Products Pipeline Company (the "Company" or "General
Partner"), an indirect wholly-owned subsidiary of Duke Energy Corporation ("Duke
Energy"), owns a 1.0101% general partner interest in the Partnership. The
Company, as general partner, performs all management and operating functions
required for the Partnership pursuant to the Agreement of Limited Partnership of
TE Products Pipeline Company, Limited Partnership (the "Partnership Agreement").
The general partner is reimbursed by the Partnership for all reasonable direct
and indirect expenses incurred in managing the Partnership.

         The accompanying unaudited consolidated financial statements reflect
all adjustments, which are, in the opinion of management, of a normal and
recurring nature and necessary for a fair statement of the financial position of
the Partnership as of March 31, 1999, and the results of operations and cash
flows for the periods presented. The results of operations for the three months
ended March 31, 1999, are not necessarily indicative of results of operations
for the full year 1999. The interim financial statements should be read in
conjunction with the Partnership's consolidated financial statements and notes
thereto presented in the TE Products Pipeline Company, Limited Partnership
Annual Report on Form 10-K for the year ended December 31, 1998. Certain amounts
from the prior year have been reclassified to conform to current presentation.

         The Partnership has one business segment: the transportation, storage
and terminaling of refined products and liquefied petroleum gases ("LPGs"). The
Partnership's interstate transportation operations, including rates charged to
customers, are subject to regulations prescribed by the Federal Energy
Regulatory Commission ("FERC"). Refined products and LPGs are referred to
herein, collectively, as "petroleum products" or "products."

NOTE 2. RELATED PARTY TRANSACTIONS

         Effective March 31, 1998, TEPPCO Colorado, LLC ("TEPPCO Colorado"), a
wholly owned subsidiary of the Partnership, purchased two fractionation
facilities located in Weld County, Colorado, from Duke Energy Field Services,
Inc. ("DEFS"), a wholly-owned subsidiary of Duke Energy. TEPPCO Colorado and
DEFS entered into a twenty year Fractionation Agreement, whereby TEPPCO Colorado
will receive a variable fee for all fractionated volumes delivered to DEFS. The
purchase price of these transactions was $40 million. Intangible assets include
$38 million of value assigned to the Fractionation Agreement, which will be
amortized on a straight-line method over the term of the Fractionation
Agreement. The remaining purchase price of $2.0 million was allocated to the
fractionator facilities purchased. TEPPCO Colorado and DEFS also entered into a
Operations and Management Agreement, whereby DEFS will operate and maintain the
fractionation facilities. TEPPCO Colorado will pay DEFS a set volumetric rate
for all fractionated volumes delivered to DEFS. As the transactions occurred as
of March 31, 1998, no effect of these transactions was included in the
Partnership's consolidated statements of income for the quarter ended March 31,
1998.

NOTE 3.  INVESTMENTS

SHORT-TERM INVESTMENTS

         The Partnership routinely invests cash in liquid short-term investments
as part of it cash management program. Investments with maturities at date of
purchase of 90 days or less are considered cash equivalents. At March 31, 1999,
short-term investments included $3.3 million of investment-grade corporate
notes, which mature within one year. Such investments at March 31, 1999 included
a $0.9 million investment in Duke Power Company





                                       5
<PAGE>   6

                TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP

            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)


corporate notes. All short-term investments are classified as held-to-maturity
securities and are stated at amortized cost. The aggregate fair value of such
securities approximates amortized cost at March 31, 1999.

LONG-TERM INVESTMENTS

         At March 31, 1999, the Partnership had $4.7 million invested in
investment-grade corporate notes, which have varying maturities through
2004. These securities are classified as held-to-maturity securities and are
stated at amortized cost. The aggregate fair value of such securities
approximates amortized cost at March 31, 1999.

NOTE 4.  INVENTORIES

         Inventories are carried at the lower of cost (based on weighted average
cost method) or market. The major components of inventories were as follows (in
thousands):

<TABLE>
<CAPTION>
                                                            MARCH 31,      DECEMBER 31,
                                                              1999           1998
                                                           ------------   ------------
<S>                                                        <C>            <C>         
    Gasolines ..........................................   $      3,901   $      4,224
    Propane ............................................            881          1,503
    Butanes ............................................          1,573          1,654
    MTBE ...............................................            596            641
    Other products .....................................          2,192          1,704
    Materials and supplies .............................          3,611          3,666
                                                           ------------   ------------
              Total ....................................   $     12,754   $     13,392
                                                           ============   ============
</TABLE>

         The costs of inventories were lower than market at March 31, 1999, and
December 31, 1998.

NOTE 5.  LONG TERM DEBT

SENIOR NOTES

         On January 27, 1998, the Partnership completed the issuance of $180
million principal amount of 6.45% Senior Notes due 2008, and $210 million
principal amount of 7.51% Senior Notes due 2028 (collectively the "Senior
Notes"). The 6.45% Senior Notes due 2008 are not subject to redemption prior to
January 15, 2008. The 7.51% Senior Notes due 2028 may be redeemed at any time
after January 15, 2008, at the option of the Partnership, in whole or in part,
at a premium. Net proceeds from the issuance of the Senior Notes totaled
approximately $386 million and was used to repay in full the $61.0 million
principal amount of the 9.60% Series A First Mortgage Notes, due 2000, and the
$265.5 million principal amount 10.20% Series B First Mortgage Notes, due 2010.
The premium for the early redemption of the First Mortgage Notes totaled $70.1
million. The Partnership recorded an extraordinary charge of $73.5 million
during the first quarter of 1998, which represents the redemption premium of
$70.1 million and unamortized debt issue costs related to the First Mortgage
Notes of $3.4 million.

         The Senior Notes do not have sinking fund requirements. Interest on the
Senior Notes is payable semiannually in arrears on January 15 and July 15 of
each year. The Senior Notes are unsecured obligations of the Partnership and
will rank on a parity with all other unsecured and unsubordinated indebtedness
of the Partnership. The indenture governing the Senior Notes contains covenants,
including, but not limited to, covenants limiting (i) the creation of liens
securing indebtedness and (ii) sale and leaseback transactions. However, the
indenture does not limit the Partnership's ability to incur additional
indebtedness.



                                       6
<PAGE>   7
                TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP

            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)


OTHER LONG TERM DEBT

         In connection with the purchase of the fractionation assets from DEFS
as of March 31, 1998, TEPPCO Colorado received a $38 million bank loan from
SunTrust Bank. Proceeds from the loan were received on April 21, 1998. TEPPCO
Colorado paid interest to DEFS at a per annum rate of 5.75% on the amount of the
total purchase price outstanding for the period from March 31, 1998 until April
21, 1998. The SunTrust loan bears interest at a rate of 6.53%, which is payable
quarterly beginning in July 1998. The principal balance of the loan is payable
in full on April 21, 2001. The Partnership is guarantor on the loan.

NOTE 6.  CASH DISTRIBUTIONS

         The Partnership makes quarterly cash distributions of all of its
Available Cash, generally defined as consolidated cash receipts less
consolidated cash disbursements and cash reserves established by the general
partner in its sole discretion. Generally, distributions are made 98.9899% to
the Parent Partnership and 1.0101% to the general partner.

         On February 5, 1999, the Partnership paid a cash distribution of $14.7
million for the fourth quarter of 1999. Additionally, on April 16, 1999, the
Partnership declared a cash distribution of $14.7 million for the quarter ended
March 31, 1999. The distribution will be paid on May 7, 1999.

NOTE 7.  COMMITMENTS AND CONTINGENCIES

         The Partnership is involved in various claims and legal proceedings
incidental to its business. In the opinion of management, these claims and legal
proceedings will not have a material adverse effect on the Partnership's
consolidated financial position or results of operations.

         The operations of the Partnership are subject to federal, state and
local laws and regulations relating to protection of the environment. Although
the Partnership believes its operations are in material compliance with
applicable environmental regulations, risks of significant costs and liabilities
are inherent in pipeline operations, and there can be no assurance that
significant costs and liabilities will not be incurred. Moreover, it is possible
that other developments, such as increasingly strict environmental laws and
regulations and enforcement policies thereunder, and claims for damages to
property or persons resulting from the operations of the pipeline system, could
result in substantial costs and liabilities to the Partnership. The Partnership
does not anticipate that changes in environmental laws and regulations will have
a material adverse effect on its financial position, operations or cash flows in
the near term.

         The Partnership and the Indiana Department of Environmental Management
("IDEM") have entered into an Agreed Order that will ultimately result in a
remediation program for any on-site and off-site groundwater contamination
attributable to the Partnership's operations at the Seymour, Indiana, terminal.
A Feasibility Study, which includes the Partnership's proposed remediation
program, has been approved by IDEM. IDEM will issue a Record of Decision
formally approving the remediation program. After the Record of Decision has
been issued, the Partnership will enter into an Agreed Order for the continued
operation and maintenance of the program. The Partnership estimates that the
costs of the remediation program being proposed by the Partnership for the
Seymour terminal will not exceed the amount accrued therefore (approximately
$0.7 million at March 31, 1999). In the opinion of the Company, the completion
of the remediation program being proposed by the Partnership, if such program is
approved by IDEM, will not have a material adverse impact on the Partnership's
financial condition, results of operations or liquidity.



                                       7
<PAGE>   8
                TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP

            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)


         In 1997, the Company initiated a program to prepare the Partnership's
process controls and business computer systems for the "Year 2000" issue.
Process controls are the automated equipment including hardware and software
systems which run operational activities. Business computer systems are the
computer hardware and software used by the Partnership. The Partnership is
utilizing both internal and external resources to identify, test, remediate or
replace all critical known or discovered non-compliant computerized systems and
applications. The Company continues to evaluate appropriate courses of
corrective action, including replacement of certain systems whose associated
costs would be recorded as assets and amortized. The Partnership has incurred
approximately $1.8 million of costs related to the Year 2000 issue. The Company
estimates the remaining amounts required to address the Year 2000 issue will be
as much as approximately $3.5 million. A portion of such costs would have been
incurred as part of normal system and application upgrades. In certain cases,
the timing of expenditures has been accelerated due to the Year 2000 issue.
Although the Company believes this estimate to be reasonable, due to the
complexities of the Year 2000 issue, there can be no assurance that the actual
costs related to the Year 2000 issue will not be significantly greater.

         The Partnership has adopted a three-phase Year 2000 program consisting
of: Phase I Preliminary Assessment; Phase II - Detailed Assessment and
Remediation Planning; and Phase III - Remediation Activities and Testing. The
Partnership has completed Phase I; Phase II is 94% complete; and Phase III is
63% complete. The Remediation Activities and Testing of all process controls and
business computer systems are scheduled to be completed before the end of the
fourth quarter of 1999.

         With respect to its third-party relationships, the Partnership has
contacted its primary vendors, suppliers and service providers to assess their
software and hardware products previously sold to the Partnership and other
aspects of their state of Year 2000 readiness. Information continues to be
updated regularly, thus the Partnership anticipates receiving additional
information in the near future that will assist in determining the extent to
which the Partnership may be vulnerable to those third parties' failure to
identify and remediate their Year 2000 issues. However, there can be no
assurance that the systems or products of other companies, on which the
Partnership's systems rely, will be timely converted, or converted in a manner
that is compatible with the Partnership's systems, or that any such failures by
other companies would not have a material adverse effect on the Partnership.

         Despite the Partnership's determined efforts to address and remediate
its Year 2000 issue, there can be no assurance that all process controls and
business computer systems will continue without interruption through January 1,
2000 and beyond. The complexity of identifying and testing all embedded
microprocessors that are installed in hardware throughout the pipeline system
used for process or flow control, transportation, security, communication and
other systems may result in unforeseen operational system shutdowns. Although
the amount of potential liability and lost revenue cannot be estimated, failures
that result in substantial disruptions of business activities could have a
material adverse effect on the Partnership. In order to mitigate potential
disruptions, the Partnership will prepare contingency plans for its critical
systems, processes and external relationships by the end of the fourth quarter
of 1999.

         In February 1999, the Partnership announced plans to construct three
new pipelines between the Partnership's terminal in Mont Belvieu, Texas and Port
Arthur, Texas. The project includes three 12-inch diameter common-carrier
pipelines and associated facilities. Each pipeline will be approximately 70
miles in length. Upon completion, the new pipelines will transport ethylene,
propylene and natural gasoline. The anticipated completion date is the fourth
quarter of 2000. The Partnership has entered into an agreement for turnkey
construction of the pipelines and related facilities and has separately entered
into agreements for guaranteed throughput commitments. The cost of this project
is expected to total approximately $74 million. Approximately $7.1 million of
spending was included in capital expenditures during the first quarter of 1999,
with a total of approximately $44 million expected 





                                       8
<PAGE>   9

                TE PRODUCTS PIPELINE COMPANY, LIMITED PARTNERSHIP

            NOTES TO CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)
                                   (UNAUDITED)


to be incurred in 1999, and the remainder in 2000. The Partnership expects to
obtain external financing during the second quarter of 1999 for this project.

         Substantially all of the petroleum products transported and stored by
the Partnership are owned by the Partnership's customers. At March 31, 1999, the
Partnership had approximately 11.6 million barrels of products in its custody
owned by customers. The Partnership is obligated for the transportation, storage
and delivery of such products on behalf of its customers. The Partnership
maintains insurance adequate to cover product losses through circumstances
beyond its control.



                                       9
<PAGE>   10


ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

GENERAL

         The Partnership's operations consist primarily of the transportation,
storage and terminaling of petroleum products. Operations are somewhat seasonal
with higher revenues generally realized during the first and fourth quarters of
each year. Refined products volumes are generally higher during the second and
third quarters because of greater demand for gasolines during the spring and
summer driving seasons. LPGs volumes are generally higher from November through
March due to higher demand in the Northeast for propane, a major fuel for
residential heating.

         The Partnership's revenues are derived primarily from the
transportation of refined products and LPGs, the storage and short-haul shuttle
transportation of LPGs at the Mont Belvieu, Texas, complex, sale of product
inventory and other ancillary services. Labor and electric power costs comprise
the two largest operating expense items of the Partnership. Effective March 31,
1998, the Partnership's operations included the fractionation of natural gas
liquids (see Note 2 in Item 1. Related Party Transactions).

         The following information is provided to facilitate increased
understanding of the 1999 and 1998 interim consolidated financial statements and
accompanying notes presented in Item 1. Material period-to-period variances in
the consolidated statements of income are discussed under "Results of
Operations." The "Financial Condition and Liquidity" section analyzes cash flows
and financial position. Discussion included in "Other Matters" addresses key
trends, future plans and contingencies. Throughout these discussions, management
addresses items that are reasonably likely to materially affect future liquidity
or earnings.

RESULTS OF OPERATIONS

         For the quarter ended March 31, 1999, the Partnership reported net
income of $21.2 million, compared with income before an extraordinary loss of
$13.3 million for the first quarter of 1998. The extraordinary loss in 1998
resulted from a $73.5 million charge for early extinguishment of debt. The $7.9
million increase in income before the loss on debt extinguishment resulted
primarily from a $10.9 million increase in operating revenues, partially offset
by a $2.3 million increase in costs and expenses and a $0.4 million increase in
interest expense. See discussion below of factors affecting net income for the
comparative periods.

         See volume and average tariff information below:

<TABLE>
<CAPTION>
                                                 QUARTER ENDED          
                                                    MARCH 31,          PERCENTAGE
                                             -----------------------    INCREASE
                                                1999        1998       (DECREASE)
                                             ----------   ----------   ----------
<S>                                          <C>          <C>          <C>        
VOLUMES DELIVERED
(in thousands of barrels)
      Refined products                           28,155       24,511           15%
      LPGs                                       13,172       10,151           30%
      Mont Belvieu operations                     6,885        5,944           16%
                                             ----------   ----------   ----------
          Total                                  48,212       40,606           19%
                                             ==========   ==========   ==========

AVERAGE TARIFF PER BARREL
      Refined products                       $     0.91   $     0.92           (1)%
      LPGs                                         2.02         2.15           (6)%
      Mont Belvieu operations                      0.16         0.16         --
          Average system tariff per barrel   $     1.11   $     1.11         --
                                             ==========   ==========   ==========
</TABLE>





                                       10
<PAGE>   11

ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

RESULTS OF OPERATIONS - (CONTINUED)

         Refined products transportation revenues increased $3.1 million for the
quarter ended March 31, 1999, compared with the prior-year quarter, as a result
of favorable differentials caused by reduced refinery production during
maintenance turnarounds at Midwest area refineries and continued strong demand
due to economic growth. Additionally, jet fuel deliveries increased as a result
of new military supply agreements that became effective in the fourth quarter of
1998. These increases were partially offset by decreased feed stock and blend
stock deliveries in the Midwest as a result of the lower refinery production in
the region.

         LPGs transportation revenues increased $4.8 million for the quarter
ended March 31, 1999, compared with the first quarter of 1998, due to a $5.3
million increase in propane revenue, partially offset by a $0.5 million decrease
in butane revenue. Increased propane revenue resulted primarily from increased
weather-related demand in the Midwest and Northeast, coupled with lower amounts
of competing local supply. Additionally, short-haul propane transportation
deliveries on the Texas Gulf Coast increased as a result of an extended
turnaround at a petrochemical facility served by the Partnership during the
first quarter of 1998. These short-haul propane deliveries resulted in the 6%
decrease in the LPGs transportation average tariff per barrel. Butane revenues
decreased during the first quarter of 1999, compared with the prior year first
quarter, as a result of lower gasoline blending demand and unfavorable economics
versus competing Canadian supply.

         Other operating revenues increased $2.8 million during the quarter
ended March 31, 1999, as compared to the same period in 1998, due primarily to
$1.8 million of revenue recognized related to the fractionation assets acquired
effective March 31, 1998, higher propane imports received at the Partnership's
marine import facility at Providence, Rhode Island, and increased refined
products terminaling and storage revenues.

         Costs and expenses increased $2.3 million for the quarter ended March
31, 1999, compared with the first quarter of 1998, due primarily to a $1.3
million increase in operating, general and administrative expenses, a $0.7
million increase in depreciation and amortization expense, and a $0.4 million
through-put related increase in operating fuel and power expense. The increase
in operating, general and administrative expenses was primarily due to a $0.5
million increase in expenses associated with Year 2000 activities, a $0.4
million increase in rental fees from higher volume through the connection from
Colonial Pipeline at Beaumont, Texas, increased pipeline maintenance activity
and $0.2 million of expense related to the fractionator facilities acquired on
March 31, 1998. These increases in operating, general and administrative
expenses were partially offset by lower insurance expenses during the first
quarter of 1999. Depreciation and amortization expense increased as a result of
amortization of the value assigned to the Fractionation Agreement beginning on
March 31, 1998, and capital additions placed in service.

         Interest expense increased $0.4 million during the first quarter of
1999, compared with the first quarter of 1998, due to interest expense on the
$38.0 million term-loan used to finance the purchase of the fractionation assets
on March 31, 1998, partially offset by lower interest expense resulting from the
refinancing of the First Mortgage Notes with the Senior Notes, which occurred on
January 27, 1998.

         Other income - net decreased during the first quarter of 1999, compared
with the prior year, as a result of lower interest income earned on cash
investments in 1999.

FINANCIAL CONDITION AND LIQUIDITY

         Net cash from operations for the quarter ended March 31, 1999, totaled
$15.4 million, comprised of $28.0 million of income before charges for
depreciation and amortization, partially offset by $12.6 million used for
working capital changes. This compares with cash flows from operations of $14.0
million for the quarter ended March 31, 1998, comprised of $19.3 million of
income before extraordinary loss on early extinguishment of debt and charges for
depreciation and amortization, partially offset by $5.3 million used for working
capital changes. The



                                       11
<PAGE>   12

ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

FINANCIAL CONDITION AND LIQUIDITY - (CONTINUED)

increase in cash used for working capital changes during the first quarter of
1999, as compared with the first quarter of 1998, resulted primarily from higher
trade receivable balances existing at March 31, 1999. Net cash from operations
for the quarter ended March 31, 1999 included interest payments related to the
Senior Notes and the term loan of $14.3 million. Net cash from operations for
the quarter ended March 31, 1998 included interest payments related to the First
Mortgage Notes of $12.8 million in connection with repayment of the outstanding
balance of the First Mortgage Notes.

         Cash flows used in investing activities during the first quarter of
1999 included $11.1 million of capital expenditures and $1.2 million of
additional cash investments. These decreases of cash were partially offset by
$3.0 million of proceeds from maturities of cash investments. Cash flows used in
investing activities during the first quarter of 1998 included $4.9 million of
capital expenditures and $2.0 million as the initial cash payment of the
purchase price of the fractionation assets and related intangible assets.

         In February 1999, the Partnership announced plans to construct three
new pipelines between the Partnership's terminal in Mont Belvieu, Texas and Port
Arthur, Texas. The project includes three 12-inch diameter common-carrier
pipelines and associated facilities. Each pipeline will be approximately 70
miles in length. Upon completion, the new pipelines will transport ethylene,
propylene and natural gasoline. The anticipated completion date is the fourth
quarter of 2000. The Partnership has entered into an agreement for turnkey
construction of the pipelines and related facilities and has separately entered
into agreements for guaranteed throughput commitments. The cost of this project
is expected to total approximately $74 million. Approximately $7.1 million of
spending was included in capital expenditures during the first quarter of 1999,
with a total of approximately $44 million expected to be incurred in 1999, and
the remainder in 2000. The Partnership expects to obtain external financing
during the second quarter of 1999 for this project.

         Exclusive of the pipeline construction between Mont Belvieu and Port
Arthur, the Partnership estimates that the remaining capital expenditures for
1999 will total approximately $21 million. Substantially all expenditures are
expected to be used for life-cycle replacements and to upgrade current
facilities. The Partnership revises capital spending estimates periodically in
response to changes in cash flows and operations.

         On January 27, 1998, the Partnership completed the issuance of $180
million principal amount of 6.45% Senior Notes due 2008, and $210 million
principal amount of 7.51% Senior Notes due 2028 (collectively the "Senior
Notes"). The 6.45% Senior Notes due 2008 are not subject to redemption prior to
January 15, 2008. The 7.51% Senior Notes due 2028 may be redeemed at any time
after January 15, 2008, at the option of the Partnership, in whole or in part,
at a premium. Net proceeds from the issuance of the Senior Notes totaled
approximately $386 million and was used to repay in full the $61.0 million
principal amount of the 9.60% Series A First Mortgage Notes, due 2000, and the
$265.5 million principal amount of the 10.20% Series B First Mortgage Notes, due
2010. The premium for the early redemption of the First Mortgage Notes totaled
$70.1 million. The repayment of the First Mortgage Notes and the issuance of the
Senior Notes reduced the level of cash required for debt service until 2008. The
Partnership recorded an extraordinary charge of $73.5 million during the first
quarter of 1998, which represents the redemption premium of $70.1 million and
unamortized debt issue costs related to the First Mortgage Notes of $3.4
million.

         The Senior Notes do not have sinking fund requirements. Interest on the
Senior Notes is payable semiannually in arrears on January 15 and July 15 of
each year, commencing July 15, 1998. The Senior Notes are unsecured obligations
of the Partnership and rank on a parity with all other unsecured and
unsubordinated indebtedness of the Partnership. The indenture governing the
Senior Notes contains covenants, including, but not limited to, covenants
limiting (i) the creation of liens securing indebtedness and (ii) sale and
leaseback transactions. However, the indenture does not limit the Partnership's
ability to incur additional indebtedness.



                                       12
<PAGE>   13
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

FINANCIAL CONDITION AND LIQUIDITY - (CONTINUED)

         In connection with the purchase of the fractionation assets from DEFS
as of March 31, 1998, TEPPCO Colorado received a $38 million bank loan from
SunTrust Bank. Proceeds from the loan were received on April 21, 1998, and
therefore were not included on the consolidated statement of cash flows as of
March 31, 1998. The loan bears interest at a rate of 6.53%, which is payable
quarterly beginning in July 1998. The principal balance of the loan is payable
in full on April 21, 2001. The Partnership is guarantor on the loan. TEPPCO
Colorado paid interest to DEFS at a per annum rate of 5.75% on the amount of the
total purchase price outstanding for the period from March 31, 1998 until April
21, 1998.

         On February 5, 1999, the Partnership paid a cash distribution of $14.7
million for the fourth quarter of 1998. Additionally, on April 16, 1999, the
Partnership declared a cash distribution of $14.7 million for the quarter ended
March 31, 1999. The distribution will be paid on May 7, 1999.

OTHER MATTERS

         The operations of the Partnership are subject to federal, state and
local laws and regulations relating to protection of the environment. Although
the Partnership believes its operations are in material compliance with
applicable environmental regulations, risks of significant costs and liabilities
are inherent in pipeline operations, and there can be no assurance that
significant costs and liabilities will not be incurred. Moreover, it is possible
that other developments, such as increasingly strict environmental laws and
regulations and enforcement policies thereunder, and claims for damages to
property or persons resulting from the operations of the pipeline system, could
result in substantial costs and liabilities to the Partnership. The Partnership
does not anticipate that changes in environmental laws and regulations will have
a material adverse effect on its financial position, operations or cash flows in
the near term.

         The Partnership and the Indiana Department of Environmental Management
("IDEM") have entered into an Agreed Order that will ultimately result in a
remediation program for any on-site and off-site groundwater contamination
attributable to the Partnership's operations at the Seymour, Indiana, terminal.
A Feasibility Study, which includes the Partnership's proposed remediation
program, has been approved by IDEM. IDEM will issue a Record of Decision
formally approving the remediation program. After the Record of Decision has
been issued, the Partnership will enter into an Agreed Order for the continued
operation and maintenance of the program. The Partnership estimates that the
costs of the remediation program being proposed by the Partnership for the
Seymour terminal will not exceed the amount accrued therefore (approximately
$0.7 million at March 31, 1999). In the opinion of the Company, the completion
of the remediation program being proposed by the Partnership, if such program is
approved by IDEM, will not have a material adverse impact on the Partnership's
financial condition, results of operations or liquidity.

         In 1997, the Company initiated a program to prepare the Partnership's
process controls and business computer systems for the "Year 2000" issue.
Process controls are the automated equipment including hardware and software
systems which run operational activities. Business computer systems are the
computer hardware and software used by the Partnership. The Partnership is
utilizing both internal and external resources to identify, test, remediate or
replace all critical known or discovered non-compliant computerized systems and
applications. The Company continues to evaluate appropriate courses of
corrective action, including replacement of certain systems whose associated
costs would be recorded as assets and amortized. The Partnership has incurred
approximately $1.8 million of costs related to the Year 2000 issue. The Company
estimates the remaining amounts required to address the Year 2000 issue will be
as much as approximately $3.5 million. A portion of such costs would have been
incurred as part of normal system and application upgrades. In certain cases,
the timing of expenditures has been accelerated due to the Year 2000 issue.
Although the Company believes this estimate to be reasonable, due to the
complexities of the Year 2000 issue, there can be no assurance that the actual
costs related to the Year 2000 issue will not be significantly greater.



                                       13
<PAGE>   14


ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS

OTHER MATTERS - (CONTINUED)

         The Partnership has adopted a three-phase Year 2000 program consisting
of: Phase I Preliminary Assessment; Phase II - Detailed Assessment and
Remediation Planning; and Phase III - Remediation Activities and Testing. The
Partnership has completed Phase I; Phase II is 94% complete; and Phase III is
63% complete. The Remediation Activities and Testing of all process controls and
business computer systems are scheduled to be completed before the end of the
fourth quarter of 1999.

         With respect to its third-party relationships, the Partnership has
contacted its primary vendors, suppliers and service providers to assess their
software and hardware products previously sold to the Partnership and other
aspects of their state of Year 2000 readiness. Information continues to be
updated regularly, thus the Partnership anticipates receiving additional
information in the near future that will assist in determining the extent to
which the Partnership may be vulnerable to those third parties' failure to
identify and remediate their Year 2000 issues. However, there can be no
assurance that the systems or products of other companies, on which the
Partnership's systems rely, will be timely converted, or converted in a manner
that is compatible with the Partnership's systems, or that any such failures by
other companies would not have a material adverse effect on the Partnership.

         Despite the Partnership's determined efforts to address and remediate
its Year 2000 issue, there can be no assurance that all process controls and
business computer systems will continue without interruption through January 1,
2000 and beyond. The complexity of identifying and testing all embedded
microprocessors that are installed in hardware throughout the pipeline system
used for process or flow control, transportation, security, communication and
other systems may result in unforeseen operational system shutdowns. Although
the amount of potential liability and lost revenue cannot be estimated, failures
that result in substantial disruptions of business activities could have a
material adverse effect on the Partnership. In order to mitigate potential
disruptions, the Partnership will prepare contingency plans for its critical
systems, processes and external relationships by the end of the fourth quarter
of 1999.

         The matters discussed herein include "forward-looking statements"
within the meaning of various provisions of the Securities Act of 1933 and the
Securities Exchange Act of 1934. All statements, other than statements of
historical facts, included in this document that address activities, events or
developments that the Partnership expects or anticipates will or may occur in
the future, including such things as estimated future capital expenditures
(including the amount and nature thereof), business strategy and measures to
implement strategy, competitive strengths, goals, expansion and growth of the
Partnership's business and operations, plans, references to future success,
references to intentions as to future matters and other such matters are
forward-looking statements. These statements are based on certain assumptions
and analyses made by the Partnership in light of its experience and its
perception of historical trends, current conditions and expected future
developments as well as other factors it believes are appropriate under the
circumstances. However, whether actual results and developments will conform
with the Partnership's expectations and predictions is subject to a number of
risks and uncertainties, including general economic, market or business
conditions, the opportunities (or lack thereof) that may be presented to and
pursued by the Partnership, competitive actions by other pipeline companies,
changes in laws or regulations, and other factors, many of which are beyond the
control of the Partnership. Consequently, all of the forward-looking statements
made in this document are qualified by these cautionary statements and there can
be no assurance that actual results or developments anticipated by the
Partnership will be realized or, even if substantially realized, that they will
have the expected consequences to or effect on the Partnership or its business
or operations. For additional discussion of such risks and uncertainties, see
TE Products Pipeline Company, Limited Partnership's 1998 Annual Report on 
Form 10-K.



                                       14
<PAGE>   15

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISKS

         At March 31, 1999, the Partnership had outstanding $180 million
principal amount of 6.45% Senior Notes due 2008, and $210 million principal
amount of 7.51% Senior Notes due 2028 (collectively the "Senior Notes").
Additionally, the Partnership had a $38 million bank loan outstanding from
SunTrust Bank. The SunTrust loan bears interest at a fixed rate of 6.53% and is
payable in full in April 2001. At March 31, 1999, the estimated fair value of
the Senior Notes and the SunTrust loan was approximately $394.7 million and 
$38.7 million, respectively.

         The Partnership periodically enters into futures contracts to hedge its
exposure to price risk on product inventory transactions. Recognized gains and
losses related to futures contracts which qualify as hedges are recognized in
income when the related inventory transactions are completed. Gains and losses
related to futures contracts, to the extent settled in cash, are reported as a
component of product inventory in the consolidated balance sheet until
recognized as income. At March 31, 1999, there were no outstanding futures
contracts.





                                       15
<PAGE>   16

                          PART II. OTHER INFORMATION


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

 (a) Exhibits:

<TABLE>
<CAPTION>
     Exhibit
     Number               Description
     ------               -----------
<S>         <C> 
      3.1   Certificate of Formation of TEPPCO Colorado, LLC (Filed as Exhibit
            3.2 to Form 10-Q of TEPPCO Partners, L.P. (Commission File No.
            1-10403) for the quarter ended March 31, 1998 and incorporated
            herein by reference)

      3.2   Amended and Restated Agreement of Limited Partnership of TE Products
            Pipeline Company, Limited Partnership, effective July 21, 1998
            (Filed as Exhibit 3.2 to Form 8-K of TEPPCO Partners, L.P.
            (Commission File No. 1-10403) dated July 21, 1998 and incorporated
            herein by reference).

      4.1   Form of Indenture between TE Products Pipeline Company, Limited
            Partnership and The Bank of New York, as Trustee, dated as of
            January 27, 1998 (Filed as Exhibit 4.3 to TE Products Pipeline
            Company, Limited Partnership's Registration Statement on Form S-3
            (Commission File No. 333-38473) and incorporated herein by
            reference).

      10.1  Assignment and Assumption Agreement, dated March 24, 1988, between
            Texas Eastern Transmission Corporation and the Company (Filed as
            Exhibit 10.8 to the Registration Statement of TEPPCO Partners, L.P.
            (Commission File No. 33-32203) and incorporated herein by
            reference).

      10.2  Texas Eastern Products Pipeline Company 1997 Employee Incentive
            Compensation Plan executed on July 14, 1997 (Filed as Exhibit 10 to
            Form 10-Q of TEPPCO Partners, L.P. (Commission File No. 1-10403) for
            the quarter ended September 30, 1997 and incorporated herein by
            reference).

      10.3  Agreement Regarding Environmental Indemnities and Certain Assets
            (Filed as Exhibit 10.5 to Form 10-K of TEPPCO Partners, L.P.
            (Commission File No. 1-10403) for the year ended December 31, 1990
            and incorporated herein by reference).

      10.4  Texas Eastern Products Pipeline Company Management Incentive
            Compensation Plan executed on January 30, 1992 (Filed as Exhibit 10
            to Form 10-Q of TEPPCO Partners, L.P. (Commission File No. 1-10403)
            for the quarter ended March 31, 1992 and incorporated herein by
            reference).

      10.5  Texas Eastern Products Pipeline Company Long-Term Incentive
            Compensation Plan executed on October 31, 1990 (Filed as Exhibit
            10.9 to Form 10-K of TEPPCO Partners, L.P. (Commission File No.
            1-10403) for the year ended December 31, 1990 and incorporated
            herein by reference).

      10.6  Form of Amendment to Texas Eastern Products Pipeline Company
            Long-Term Incentive Compensation Plan (Filed as Exhibit 10.7 to the
            Partnership's Form 10-K (Commission File No. 1-10403) for the year
            ended December 31, 1995 and incorporated herein by reference).

      10.7  Employees' Savings Plan of Panhandle Eastern Corporation and
            Participating Affiliates (Effective January 1, 1991) (Filed as
            Exhibit 10.10 to the Partnership's Form 10-K (Commission File No.
            1-10403) for the year ended December 31, 1990 and incorporated
            herein by reference).

      10.8  Retirement Income Plan of Panhandle Eastern Corporation and
            Participating Affiliates (Effective January 1, 1991) (Filed as
            Exhibit 10.11 to Form 10-K of TEPPCO Partners, L.P. (Commission File
            No. 1-10403) for the year ended December 31, 1990 and incorporated
            herein by reference).

      10.9  Panhandle Eastern Corporation Key Executive Retirement Benefit
            Equalization Plan, adopted December 20, 1993; effective January 1,
            1994 (Filed as Exhibit 10.12 to Form
</TABLE>



                                       16
<PAGE>   17

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K - (CONTINUED)


<TABLE>
<CAPTION>
     Exhibit
     Number               Description
     ------               -----------
<S>         <C> 
             10-K of Panhandle Eastern Corporation (Commission File No. 1-8157)
             for the year ended December 31, 1993 and incorporated herein by
             reference).

      10.10  Employment Agreement with William L. Thacker, Jr. (Filed as Exhibit
             10 to Form 10-Q of TEPPCO Partners, L.P. (Commission File No.
             1-10403) for the quarter ended September 30, 1992 and incorporated
             herein by reference).

      10.11  Texas Eastern Products Pipeline Company 1994 Long Term Incentive
             Plan executed on March 8, 1994 (Filed as Exhibit 10.1 to Form 10-Q
             of TEPPCO Partners, L.P. (Commission File No. 1-10403) for the
             quarter ended March 31, 1994 and incorporated herein by reference).

      10.12  Panhandle Eastern Corporation Key Executive Deferred Compensation
             Plan established effective January 1, 1994 (Filed as Exhibit 10.2
             to Form 10-Q of TEPPCO Partners, L.P. (Commission File No. 1-10403)
             for the quarter ended March 31, 1994 and incorporated herein by
             reference).

      10.13  Asset Purchase Agreement between Duke Energy Field Services, Inc.
             and TEPPCO Colorado, LLC, dated March 31, 1998 (Filed as Exhibit
             10.14 to Form 10-Q of TEPPCO Partners, L.P. (Commission File No.
             1-10403) for the quarter ended March 31, 1998 and incorporated
             herein by reference).

      10.14  Credit Agreement between TEPPCO Colorado, LLC, SunTrust Bank,
             Atlanta, and Certain Lenders, dated April 21, 1998 (Filed as
             Exhibit 10.15 to Form 10-Q of TEPPCO Partners, L.P. (Commission
             File No. 1-10403) for the quarter ended March 31, 1998 and
             incorporated herein by reference).

      10.15  First Amendment to Credit Agreement between TEPPCO Colorado, LLC,
             SunTrust Bank, Atlanta, and Certain Lenders, effective June 29,
             1998 (Filed as Exhibit 10.15 to Form 10-Q of TEPPCO Partners, L.P.
             (Commission File No. 1-10403) for the quarter ended June 30, 1998
             and incorporated herein by reference).

      10.16  Form of Employment Agreement between the Company and O. Horton
             Cunningham, Ernest P. Hagan, Thomas R. Harper, David L. Langley,
             Charles H. Leonard and James C. Ruth, dated December 1, 1998 (Filed
             as Exhibit 10.20 to Form 10-K of TEPPCO Partners, L.P. (Commission
             File No. 1-10403) for the year ended December 31, 1998 and
             incorporated herein by reference).

      10.17  Agreement Between Owner and Contractor between TE Products Pipeline
             Company, Limited Partnership and Eagleton Engineering Company,
             dated February 4, 1999 (Filed as Exhibit 10.21 to Form 10-Q of
             TEPPCO Partners, L.P. (Commission File No. 1-10403) for the quarter
             ended March 31, 1999 and incorporated herein by reference).

      10.18  Services and Transportation Agreement between TE Products Pipeline
             Company, Limited Partnership and Fina Oil and Chemical Company,
             BASF Corporation and BASF Fina Petrochemical Limited Partnership,
             dated February 9, 1999 (Filed as Exhibit 10.22 to Form 10-Q of
             TEPPCO Partners, L.P. (Commission File No. 1-10403) for the quarter
             ended March 31, 1999 and incorporated herein by reference).

      10.19  Call Option Agreement, dated February 9, 1999 (Filed as Exhibit
             10.23 to Form 10-Q of TEPPCO Partners, L.P. (Commission File No.
             1-10403) for the quarter ended March 31, 1999 and incorporated
             herein by reference).

      27*    Financial Data Schedules as of and for the three months ended March
             31, 1999.
</TABLE>

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


        *    Filed herewith.

 (b) Reports on Form 8-K filed during the quarter ended March 31, 1999: None.


Items 1, 2, 3, 4 and 5 of Part II were not applicable and have been omitted.



                                       17
<PAGE>   18
                                  SIGNATURE


         Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrants have duly caused this report to be signed on its behalf by the
undersigned duly authorized officer and principal financial officer.


                              TE Products Pipeline Company, Limited Partnership
                              (Registrant)

                              By:  Texas Eastern Products Pipeline Company,
                                   General Partner



                                        /s/ CHARLES H. LEONARD              
                              ----------------------------------------------
                                            Charles H. Leonard              
                              Senior Vice President, Chief Financial Officer
                                              and Treasurer                 
                               




Date:  May 6, 1999


                                       18
<PAGE>   19
                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
     Exhibit
     Number               Description
     ------               -----------
<S>         <C> 
      3.1   Certificate of Formation of TEPPCO Colorado, LLC (Filed as Exhibit
            3.2 to Form 10-Q of TEPPCO Partners, L.P. (Commission File No.
            1-10403) for the quarter ended March 31, 1998 and incorporated
            herein by reference)

      3.2   Amended and Restated Agreement of Limited Partnership of TE Products
            Pipeline Company, Limited Partnership, effective July 21, 1998
            (Filed as Exhibit 3.2 to Form 8-K of TEPPCO Partners, L.P.
            (Commission File No. 1-10403) dated July 21, 1998 and incorporated
            herein by reference).

      4.1   Form of Indenture between TE Products Pipeline Company, Limited
            Partnership and The Bank of New York, as Trustee, dated as of
            January 27, 1998 (Filed as Exhibit 4.3 to TE Products Pipeline
            Company, Limited Partnership's Registration Statement on Form S-3
            (Commission File No. 333-38473) and incorporated herein by
            reference).

      10.1  Assignment and Assumption Agreement, dated March 24, 1988, between
            Texas Eastern Transmission Corporation and the Company (Filed as
            Exhibit 10.8 to the Registration Statement of TEPPCO Partners, L.P.
            (Commission File No. 33-32203) and incorporated herein by
            reference).

      10.2  Texas Eastern Products Pipeline Company 1997 Employee Incentive
            Compensation Plan executed on July 14, 1997 (Filed as Exhibit 10 to
            Form 10-Q of TEPPCO Partners, L.P. (Commission File No. 1-10403) for
            the quarter ended September 30, 1997 and incorporated herein by
            reference).

      10.3  Agreement Regarding Environmental Indemnities and Certain Assets
            (Filed as Exhibit 10.5 to Form 10-K of TEPPCO Partners, L.P.
            (Commission File No. 1-10403) for the year ended December 31, 1990
            and incorporated herein by reference).

      10.4  Texas Eastern Products Pipeline Company Management Incentive
            Compensation Plan executed on January 30, 1992 (Filed as Exhibit 10
            to Form 10-Q of TEPPCO Partners, L.P. (Commission File No. 1-10403)
            for the quarter ended March 31, 1992 and incorporated herein by
            reference).

      10.5  Texas Eastern Products Pipeline Company Long-Term Incentive
            Compensation Plan executed on October 31, 1990 (Filed as Exhibit
            10.9 to Form 10-K of TEPPCO Partners, L.P. (Commission File No.
            1-10403) for the year ended December 31, 1990 and incorporated
            herein by reference).

      10.6  Form of Amendment to Texas Eastern Products Pipeline Company
            Long-Term Incentive Compensation Plan (Filed as Exhibit 10.7 to the
            Partnership's Form 10-K (Commission File No. 1-10403) for the year
            ended December 31, 1995 and incorporated herein by reference).

      10.7  Employees' Savings Plan of Panhandle Eastern Corporation and
            Participating Affiliates (Effective January 1, 1991) (Filed as
            Exhibit 10.10 to the Partnership's Form 10-K (Commission File No.
            1-10403) for the year ended December 31, 1990 and incorporated
            herein by reference).

      10.8  Retirement Income Plan of Panhandle Eastern Corporation and
            Participating Affiliates (Effective January 1, 1991) (Filed as
            Exhibit 10.11 to Form 10-K of TEPPCO Partners, L.P. (Commission File
            No. 1-10403) for the year ended December 31, 1990 and incorporated
            herein by reference).

      10.9  Panhandle Eastern Corporation Key Executive Retirement Benefit
            Equalization Plan, adopted December 20, 1993; effective January 1,
            1994 (Filed as Exhibit 10.12 to Form
</TABLE>



<PAGE>   20


<TABLE>
<CAPTION>
     Exhibit
     Number               Description
     ------               -----------
<S>         <C> 
             10-K of Panhandle Eastern Corporation (Commission File No. 1-8157)
             for the year ended December 31, 1993 and incorporated herein by
             reference).

      10.10  Employment Agreement with William L. Thacker, Jr. (Filed as Exhibit
             10 to Form 10-Q of TEPPCO Partners, L.P. (Commission File No.
             1-10403) for the quarter ended September 30, 1992 and incorporated
             herein by reference).

      10.11  Texas Eastern Products Pipeline Company 1994 Long Term Incentive
             Plan executed on March 8, 1994 (Filed as Exhibit 10.1 to Form 10-Q
             of TEPPCO Partners, L.P. (Commission File No. 1-10403) for the
             quarter ended March 31, 1994 and incorporated herein by reference).

      10.12  Panhandle Eastern Corporation Key Executive Deferred Compensation
             Plan established effective January 1, 1994 (Filed as Exhibit 10.2
             to Form 10-Q of TEPPCO Partners, L.P. (Commission File No. 1-10403)
             for the quarter ended March 31, 1994 and incorporated herein by
             reference).

      10.13  Asset Purchase Agreement between Duke Energy Field Services, Inc.
             and TEPPCO Colorado, LLC, dated March 31, 1998 (Filed as Exhibit
             10.14 to Form 10-Q of TEPPCO Partners, L.P. (Commission File No.
             1-10403) for the quarter ended March 31, 1998 and incorporated
             herein by reference).

      10.14  Credit Agreement between TEPPCO Colorado, LLC, SunTrust Bank,
             Atlanta, and Certain Lenders, dated April 21, 1998 (Filed as
             Exhibit 10.15 to Form 10-Q of TEPPCO Partners, L.P. (Commission
             File No. 1-10403) for the quarter ended March 31, 1998 and
             incorporated herein by reference).

      10.15  First Amendment to Credit Agreement between TEPPCO Colorado, LLC,
             SunTrust Bank, Atlanta, and Certain Lenders, effective June 29,
             1998 (Filed as Exhibit 10.15 to Form 10-Q of TEPPCO Partners, L.P.
             (Commission File No. 1-10403) for the quarter ended June 30, 1998
             and incorporated herein by reference).

      10.16  Form of Employment Agreement between the Company and O. Horton
             Cunningham, Ernest P. Hagan, Thomas R. Harper, David L. Langley,
             Charles H. Leonard and James C. Ruth, dated December 1, 1998 (Filed
             as Exhibit 10.20 to Form 10-K of TEPPCO Partners, L.P. (Commission
             File No. 1-10403) for the year ended December 31, 1998 and
             incorporated herein by reference).

      10.17  Agreement Between Owner and Contractor between TE Products Pipeline
             Company, Limited Partnership and Eagleton Engineering Company,
             dated February 4, 1999 (Filed as Exhibit 10.21 to Form 10-Q of
             TEPPCO Partners, L.P. (Commission File No. 1-10403) for the quarter
             ended March 31, 1999 and incorporated herein by reference).

      10.18  Services and Transportation Agreement between TE Products Pipeline
             Company, Limited Partnership and Fina Oil and Chemical Company,
             BASF Corporation and BASF Fina Petrochemical Limited Partnership,
             dated February 9, 1999 (Filed as Exhibit 10.22 to Form 10-Q of
             TEPPCO Partners, L.P. (Commission File No. 1-10403) for the quarter
             ended March 31, 1999 and incorporated herein by reference).

      10.19  Call Option Agreement, dated February 9, 1999 (Filed as Exhibit
             10.23 to Form 10-Q of TEPPCO Partners, L.P. (Commission File No.
             1-10403) for the quarter ended March 31, 1999 and incorporated
             herein by reference).

      27*    Financial Data Schedules as of and for the three months ended March
             31, 1999.
</TABLE>

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


        *    Filed herewith.