SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549



                                    FORM 8-K

                                 CURRENT REPORT

                     PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                DATE OF REPORT (date of earliest event reported)

                                 APRIL 26, 1999

                               Halliburton Company
             (Exact name of registrant as specified in its charter)

State or other                      Commission                IRS Employer
jurisdiction                        File Number               Identification
of incorporation                                              Number

Delaware                              1-3492                  No. 75-2677995

                               3600 Lincoln Plaza
                             500 North Akard Street
                            Dallas, Texas 75201-3391
                    (Address of principal executive offices)

                         Registrant's telephone number,
                       including area code - 214/978-2600




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                       The Exhibit Index Appears on Page 4


INFORMATION TO BE INCLUDED IN REPORT Item 5. Other Events The registrant may, at its option, report under this item any events, with respect to which information is not otherwise called for by this form, that the registrant deems of importance to security holders. On April 26, 1999 registrant issued a press release entitled Halliburton Reports 1999 First Quarter pertaining, among other things, to an announcement that registrant earned $81 million ($.18 per diluted share) in the 1999 first quarter before the net cumulative effect of a change in accounting method, compared to net income of $203 million ($.46 per diluted share) earned in first quarter 1998. Registrant's 1999 first quarter revenues were $3.9 billion, down eight percent compared to a year ago. During first quarter 1999 registrant adopted the American Institute of Certified Public Accountants' Statement of Position 98-5 (SOP 98-5). As a result of the adoption of SOP 98-5 in the 1999 first quarter, registrant recognized a $19 million after tax charge ($.04 per diluted share) which brought net income to $62 million ($.14 per diluted share). Item 7. Financial Statements and Exhibits List below the financial statements, pro forma financial information and exhibits, if any, filed as part of this report. (c) Exhibits. Exhibit 20 - Press release dated April 26, 1999. Page 2 of 8 Pages The Exhibit Index Appears on Page 4

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 hereunto duly authorized. HALLIBURTON COMPANY Date: April 27, 1999 By: /s/ Susan S. Keith ------------------------------- Susan S. Keith Vice President and Secretary Page 3 of 8 Pages The Exhibit Index Appears on Page 4

EXHIBIT INDEX Exhibit Sequentially Number Description Numbered Page 20 Press Release of 5 of 8 April 26, 1999 Incorporated by Reference Page 4 of 8 Pages The Exhibit Index Appears on Page 4


FOR IMMEDIATE RELEASE      Contact: Guy T. Marcus
04/26/99                            Vice President-Investor Relations
                                    214/978-2691

                     HALLIBURTON REPORTS 1999 FIRST QUARTER

         DALLAS,  Texas -- Halliburton  Company  (NYSE:HAL) today announces that
the  company  earned  $81  million ($ .18 per  diluted  share) in the 1999 first
quarter  before  the net  cumulative  effect of a change in  accounting  method,
compared to net income of $203 million ($ . 46 per diluted  share) earned in the
year earlier first quarter.  The company's 1999 first quarter revenues were $3.9
billion, down only eight percent compared to a year ago.
         Reduced  revenues and lower  earnings for the company in the 1999 first
quarter are  attributable to petroleum  industry  customers'  sharp reduction of
spending  in response to very low crude oil and natural gas prices in the latter
part of 1998 and the 1999 first  quarter.  The poor  market  conditions  had the
greatest  impact on the financial  results of the Energy Services Group business
segment.
         During  the  1999  first  quarter   Halliburton  adopted  the  American
Institute  of  Certified  Public   Accountants'   Statement  of  Position  98-5,
"Reporting  on Costs of Start-Up  Activities  (SOP 98-5)",  which  requires such
costs to be expensed as incurred rather than being  capitalized.  As a result of
the adoption of SOP 98-5 in the 1999 first quarter, the company recognized a $19
million  after tax charge ($ .04 per diluted  share) which brought net income to
$62 million ($ .14 per diluted share).
         The Energy  Services  Group  business  segment's  revenues were down 23
percent to $1,753  million in the 1999 first  quarter,  as  compared to the 1998

                                     -more-

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Halliburton Company page 2 quarter, while activity levels as measured by the worldwide rotary rig count declined by 35 percent over the same time period. Sharp revenue reductions were experienced in both the U.S. and international areas. International areas represented more than 70 percent of the segment's revenues in the quarter. The Energy Services Group's operating income was $57 million in the 1999 first quarter, 80 percent lower than a year ago. The segment's operating margins fell from 12.4 percent in last year's quarter to 3.2 percent in the 1999 first quarter. Lower profit margins were principally driven by negative operating leverage on the lower revenues, increased price competition and discounting of services and products, and lower profitability on upstream engineering and construction work by the segment's Brown & Root Energy Services business unit. The Engineering and Construction Group business segment's revenues were $1,508 million, up 12 percent compared to the 1998 first quarter. Both of the segment's business units, Kellogg Brown & Root and Brown & Root Services, increased revenues more than 10 percent. Operating income for the segment in the 1999 first quarter was $58 million, a decline of two percent from last year's quarter, and operating margins were 3.8 percent in the 1999 first quarter compared to 4.4 percent a year ago. The lower profit margins resulted primarily from lower margin work accomplished in the United Kingdom and Asia Pacific regions during the quarter. The Dresser Equipment Group business segment's revenues of $663 million in the 1999 first quarter were six percent higher than the 1998 quarter. Operating income was $54 million for the quarter, an increase of 38 percent compared to last year's first quarter. Operating margins increased to 8.1 percent in the 1999 first quarter compared to 6.3 percent in the last year's quarter. Improved activity in the U.S., which represented 50 percent of 1999 first quarter revenues compared to 40 percent last year, contributed to the improved financial performance of the segment. -more- Page 6 of 8 Pages The Exhibit Index Appears on Page 4

Halliburton Company page 3 Dick Cheney, Halliburton Company's chief executive officer, commented, "As I've said previously, 1999 is going to be a tough year for the oil services industry. But recent actions by OPEC and the improvement of oil and natural gas prices gives us reason to believe customer spending will pick up late this year or early in 2000. During the 1999 first quarter, the company reduced employment levels by about an additional 10 percent and consolidated many facilities to reduce our cost structure to better meet the needs of our markets. With our more efficient organization and a strong technological base I am optimistic about opportunities for future growth." Halliburton Company, founded in 1919, is the world's largest provider of products and services to the petroleum and energy industries. The company serves its customers with a broad range of products and services through its Energy Services Group, Engineering and Construction Group and Dresser Equipment Group business segments. The company's World Wide Web site can be accessed at http://www.halliburton.com. ### Page 7 of 8 Pages The Exhibit Index Appears on Page 4

HALLIBURTON COMPANY Consolidated Statements of Income (Unaudited) Quarter Ended March 31 1999 1998 Millions of dollars except per share data Revenues Energy Services Group $ 1,753 $ 2,285 Engineering and Construction Group 1,508 1,347 Dresser Equipment Group 663 623 ----------- ----------- Total revenues $ 3,924 $ 4,255 ----------- ----------- ----------- ----------- Operating income Energy Services Group $ 57 $ 283 Engineering and Construction Group 58 59 Dresser Equipment Group 54 39 General corporate (17) (20) ----------- ----------- Total operating income 152 361 Interest expense (36) (30) Interest income 32 7 Foreign currency losses, net (1) - Other nonoperating, net 2 - ----------- ----------- Income before income taxes, minority interests, and change in accounting method 149 338 Provision for income taxes (60) (128) Minority interest in net income of subsidiaries (8) (7) ----------- ----------- Income before accounting change 81 203 Cumulative effect of change in accounting method, net (19) - ----------- ----------- Net income $ 62 $ 203 ----------- ----------- ----------- ----------- Basic income per share: Before change in accounting method $ 0.18 $ 0.46 Change in accounting method (0.04) - ----------- ----------- Net income $ 0.14 $ 0.46 Diluted income per share: Before change in accounting method $ 0.18 $ 0.46 Change in accounting method (0.04) - ----------- ----------- Net income $ 0.14 $ 0.46 Basic average common shares outstanding 440 438 Diluted average common shares outstanding 442 443 Prior year restated for the acquisition of Dresser Industries, Inc., which has been accounted for as a pooling of interests. Page 8 of 8 Pages The Exhibit Index Appears on Page 4