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)

                                   MAY 2, 2000

                               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 May 2, 2000 registrant issued a press release entitled "Halliburton Pioneers Revolutionary Drilling and Intervention System," pertaining to, among other things, the announcement by registrant's business unit, Halliburton Energy Services (HES), that the trials of HES' new technology, the Anaconda Advanced Well Construction System, have successfully been completed. The system will have a major impact on the exploration, development and production of oil and gas, especially offshore, by enabling customers to find and develop isolated pockets of oil and gas. 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 May 2, 2000. Page 2 of 9 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: May 4, 2000 By: /s/ Susan S. Keith ------------------------------- Susan S. Keith Vice President and Secretary Page 3 of 9 Pages The Exhibit Index Appears on Page 4

EXHIBIT INDEX Exhibit Sequentially Number Description Numbered Page 20 Press Release of 5 of 9 May 2, 2000 Incorporated by Reference Page 4 of 9 Pages The Exhibit Index Appears on Page 4

FOR IMMEDIATE RELEASE                       CONTACT:  Dirk Vande Beek or
May 2, 2000                                           Wendy Hall
                                                      Halliburton Company
                                                      (713) 676-4371 office
                                                      (713) 962-7281 cellular
                                                      (713) 598-6752 cellular

                             AND INTERVENTION SYSTEM

            Real Time Solutions a Reality with Anaconda (TM) Technology

DALLAS,  Texas - Halliburton  Energy  Services  (HES)  announced  today that the
initial trials of its revolutionary  new technology,  the Anaconda Advanced Well
Construction  System,  have successfully  been completed.  Based on breakthrough
advances in composite  materials,  telemetry and control  sciences,  this system
will have a major impact on the  exploration,  development and production of oil
and gas, especially offshore.  Halliburton Energy Services is a business unit of
Halliburton Company (NYSE: HAL).
         Halliburton, along with Statoil of Norway, developed the first phase of
this unique  technology  to develop  inaccessible  reserves in Statoil's  mature
North Sea Fields.  In less than 27 months,  Halliburton  and Statoil  produced a
complete  fit-for-purpose  system,  called Anaconda.  This digitally  controlled
system uses a carbon-fiber  composite umbilical tubing,  called  SmartPipe(TM) ,
and a  downhole  Advanced  Drilling,  Evaluation  and  Propulsion  Tool  (ADEPT)
assembly. The result is a true leap forward in well construction technology.  It
is  lighter,  safer,  requires  less  space and fewer  people  to  operate  than
alternative  systems.  Future,  large-diameter  Anaconda systems will be able to
drill more complex  wellpaths and drill extended  horizontal  distances  further
than any system ever developed.


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ANACONDA (TM) TECHNOLOGY\2 "We are pleased with our partnering efforts with Statoil on this important project," said Dave Lesar, president, Halliburton Company. "Anaconda's breakthrough technology will enable our customers to increase recoverable reserves while reducing the cost of recovered hydrocarbon units. This is the first real step change in well construction and intervention processes in over 20 years. The combination of several existing and many new technologies will reduce our customers' operating costs and capital spending." The System With the Anaconda system, oil companies will have a new capability to find and develop isolated pockets of oil and gas. The system is fully enabled with Halliburton's real-time data transmission technology, so personnel will be able to make instantaneous drilling decisions from anywhere in the world. "Anaconda will change the way wells are drilled. Geologists and geophysicists will participate in operations more than ever before by remotely directing the path of the well. The amount of real time data is enormous, several thousand times greater than is currently achievable, so precise placement of the well bore will be possible within a given hydrocarbon zone. The ability to transmit electrical power and commands through the pipe adds tremendous versatility and control to the drilling process, so well control is improved and many hazardous conditions can be avoided. This technology will bring together formation evaluation experts, drilling engineers, reservoir engineers, geologists and geophysicists to make better decisions, " said Jody Powers, president, Halliburton Energy Services. "Anaconda wells will be guided using real-time updates of the earth model and, with the instantaneous control capability, we can make the assembly almost turn on a dime, allowing us to probe for additional reserves or to access multiple reservoirs. No one else can do that," added Powers. -more- Page 6 of 9 Pages The Exhibit Index Appears on Page 4

ANACONDA (TM) TECHNOLOGY\3 "Anaconda utilizes state-of-the-art information technology for system control, telemetry and real-time communication which enables the oil companies to make rapid decisions in real time from either the drilling location or remotely. This makes possible the efficient real-time collaboration of multidisciplinary teams regardless of their proximity to the drilling operation such that reservoir assets are optimized through better decisions," said Jim Terry, inventor and director of the Anaconda Project. New Technology The major components of the system are the fully automated surface equipment, the SmartPipe with embedded conductors and the ADEPT bottomhole assembly. Surface equipment in the new system includes a control center, SmartPipe injector and reel, a tower and pipehandling system, blowout preventers, and a digital control and data-acquisition system. In the control center a three-man team operates the entire system - a "pilot" to run the equipment, a systems engineer to maintain system integrity and a "navigation engineer" who interprets the sensor data, builds a detailed subsurface map and guides the wellpath accordingly. When required, any of these functions can be performed remotely. Anaconda's SmartPipe, jointly developed by Halliburton and Fiberspar Spoolable Products, is manufactured in a continuous coil using a tough laminate of carbon-fiber and other advanced materials. Under most drilling conditions the pipe is nearly buoyant, a big advantage in extended reach drilling applications. Also, the reeled pipe eliminates many of the hazardous pipe-handling operations common with jointed steel drill pipe. The first Anaconda system uses a 2-7/8 in. Outer Diameter (OD) SmartPipe with embedded conductors that relay two-way data between the control center and the subsurface assembly. -more- Page 7 of 9 Pages The Exhibit Index Appears on Page 4

ANACONDA (TM) TECHNOLOGY\4 The ADEPT bottomhole assembly measures borehole and formation parameters, orients the borehole in 3D space, provides the mechanical forces to drill the hole and uses the industry's first open system subsurface propulsion system. With the propulsion system, no mechanical force is required from the surface equipment to convey the pipe into or out of the well. Instead, the pipe can be propelled by downhole hydraulic forces applied by the ADEPT assembly whenever necessary. Phases of the Project Research resulted in a vision of three evolving systems, each one progressively building on the technological accomplishments of the last. System 1, which was developed to meet Statoil's needs in the North Sea, uses a 2-7/8-in. OD SmartPipe and a 3-1/8 in. OD ADEPT assembly. Development will commence soon on a system which will be capable of constructing larger well diameters and achieving measured depths of up to 50,000 feet. Applications for this system will include minimizing the number of offshore structures and associated capital expenditures, drilling exploration wells in deepwater environments, subsea development wells and minimum-diameter, high-rate production wells. "We feel confident this technology will change the way our customers exploit reserves, increase ultimate recoveries and extend the life of mature fields," said Terry. "The next phase of the project is to apply proven System 1 technology to the next generation of Anaconda which will be capable of drilling and completing larger well bores. It will likely be funded in part by several other interested operators. We look forward to working in close collaboration with our customers in an effort to maximize the versatility and applicability of the Anaconda system for their assets." -more- Page 8 of 9 Pages The Exhibit Index Appears on Page 4

ANACONDA (TM) TECHNOLOGY\5 Initial Testing of the System The Anaconda well-construction system is undergoing extensive testing at the Halliburton Research and Development Center in Duncan, Oklahoma, prior to commercial deployment. To date, the system has successfully concluded eight months of tests in a horizontal flow loop and in the test well. The SmartPipe endured more than 50 times the number of stress cycles that are usually considered acceptable for steel coiled tubing with equivalent diameter. "The first commercial deployment will be in the Gulf of Mexico region," said Terry. "Statoil and Halliburton have agreed that the first few commercial wells will be drilled in the U.S. to prove up all the components of the system before going to Norway." Halliburton Energy Services provides products, services, and integrated solutions for oil and gas exploration, development, and production. Capabilities range from the initial evaluation of producing formations to drilling, completion, production enhancement, and well maintenance - for a single well or an entire field. With over 300 service centers in more than 90 countries, Halliburton possesses the global perspective that is increasingly important for energy exploration and production. Founded in 1919, Halliburton Company is the world's leading diversified energy services, engineering, construction, maintenance and energy equipment company. In 1999, Halliburton's consolidated revenues were $14.9 billion and it conducted business with a workforce of approximately 100,000 in more than 120 countries. The company's World Wide Web site can be accessed at # # # Note: In accordance with the Safe Harbor provisions of the Private Securities Litigation Reform Act of 1995, Halliburton Company cautions that statements in this press release which are forward looking and which provide other than historical information involve risks and uncertainties that may impact the company's actual results of operations. Please see Halliburton's Form 10-K for the year ended December 31, 1999 for a more complete discussion of such risk factors. Page 9 of 9 Pages The Exhibit Index Appears on Page 4