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)

                                  JULY 22, 1998

                               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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         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 July 22, 1998 registrant issued a press release entitled Halliburton
 1998 Second Quarter Net Income Up 34 Percent pertaining, among other things, to
 an  announcement  that  registrant's  1998 second  quarter net income of $136.5
 million  increased  34 percent  compared to $101.9  million  earned in the 1997
 second quarter. Registrant's consolidated revenues were $2,475.6 million in the
 1998 second quarter, an increase of 11 percent over last year's second quarter.
 For the six month period ended June 30, 1998,  net income  increased 38 percent
 to $254.3 million while revenues were 17 percent higher than the 1997 six month
 period.

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 July 22, 1998.




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                                   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:    July 23, 1998              By:  /s/  Susan S. Keith
                                        ---------------------------------
                                        Susan S. Keith
                                        Vice President and Secretary




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                                  EXHIBIT INDEX



Exhibit                                                       Sequentially
Number                     Description                        Numbered Page

20                         Press Release of                   5 of 7
                           July 22, 1998
                           Incorporated by Reference





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FOR IMMEDIATE RELEASE            Contact: Guy T. Marcus
07/22/98                                  Vice President-Investor Relations
                                          (214) 978-2691

            HALLIBURTON 1998 SECOND QUARTER NET INCOME UP 34 PERCENT

         DALLAS,  Texas -- Halliburton  Company  (NYSE:HAL)  reports 1998 second
quarter net income of $136.5 million ($ .51 per share  diluted),  an increase of
34 percent  compared to $101.9 million ($ .40 per share  diluted)  earned in the
1997 second quarter. Strong profitability  improvements were experienced by both
of the company's business segments. Halliburton's consolidated revenues totalled
$2,475.6 million in the 1998 second quarter,  11 percent higher than last year's
second quarter.
         For the six month period ending June 30, 1998, net income  increased 38
percent to $254.3  million  ($. 95 per share  diluted)  while  revenues  were 17
percent higher than the 1997 six month period.
         The Energy Group business  segment's  revenues were $1,707.0 million in
the 1998 second quarter, 17 percent higher than the year ago quarter.  Strongest
revenue growth was recorded by the Brown & Root Energy  Services and Halliburton
Energy Services business units. International revenues increased by more than 20
percent in the 1998 second quarter  compared to a year ago. The segment's strong
international presence countered slower growth in the U.S .

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         The Energy Group's 1998 second quarter  operating  income  increased 24
percent to $198.3  million  compared to the prior year  period.  With  operating
income growing faster than revenues,  the segment's operating margin improved to
11.6  percent for the 1998 second  quarter  compared to 11.0 percent in the 1997
quarter.
         The Engineering and Construction  Group business  segment's 1998 second
quarter  operating  income increased 66 percent to $49.9 million compared to the
1997 quarter,  although revenues were essentially the same as a year ago. Second
quarter   operating  income   benefitted  from  a  claim  on  a  Middle  Eastern
construction  project.  The 1998 second quarter operating margin for the segment
improved to 6.5 percent compared to last year's 3.9 percent.  Stronger financial
results  were  experienced  by  the  chemicals/olefins  and  refining  lines  of
business.
         Dick  Cheney,  Halliburton  Company's  chairman  of the board and chief
executive officer, said,  "Halliburton continues to make good financial progress
despite  uncertainty  over  future  oil  demand  and the  slowing of some of our
customers'  exploration  and  production  activities  during the  quarter.  This
uncertainty  hanging over the industry will continue to influence spending plans
for the second half of the year, as well. We are  monitoring  market  conditions
and  will  make  appropriate  adjustments  to  sustain  operating  efficiencies.
However, I believe that Halliburton's  integrated  organizational  structure and
breadth  of  capabilities  gives  us a  significant  advantage  in  serving  our


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customers,  particularly  when many of them are  facing  some  tough  decisions.
Prospects for a continuation for future growth in the company's  engineering and
construction  related activities are enhanced by a total backlog of $7.3 billion
at the end of the 1998 second  quarter,  up five  percent  compared to the first
quarter."
         Cheney continued,  "Halliburton and Dresser Industries,  Inc. (NYSE:DI)
continue to make progress towards completing  previously announced plans for the
companies to merge.  In June  shareholders  of both companies  voted in favor of
proposals  to merge the  companies  and in recent  weeks the merger has received
clearances  from the European  Commission and the Canadian Bureau of Competition
Policy.  At the present  time the  companies  have other  regulatory  filings in
process with the U.S.  Department of Justice and regulatory  agencies in certain
other countries.  The companies look forward to completing the merger during the
fall of 1998 and begin  benefitting  from  synergies  designed to enhance future
performance."
                  Halliburton  Company is one of the world's largest diversified
energy services,  engineering,  maintenance, and construction companies. Founded
in 1919,  Halliburton  provides a broad range of energy  services and  products,
industrial and marine engineering and construction services.


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HALLIBURTON COMPANY CONSOLIDATED STATEMENTS OF INCOME (UNAUDITED) Quarter Ended Six Months Ended June 30 June 30 ---------- ---------- ---------- ---------- 1998 1997 1998 1997 ---------- ---------- ---------- ---------- Millions of dollars except per share data Revenues Energy Group $ 1,707.0 $ 1,456.4 $ 3,296.2 $ 2,576.7 Engineering and Construction Group 768.6 774.7 1,534.7 1,551.9 ---------- ---------- ---------- ---------- Total revenues $ 2,475.6 $ 2,231.1 $ 4,830.9 $ 4,128.6 ========== ========== ========== ========== Operating income Energy Group $ 198.3 $ 160.1 $ 383.3 $ 277.3 Engineering and Construction Group 49.9 30.0 78.7 59.4 General corporate (9.8) (8.1) (19.6) (16.0) ---------- ---------- ---------- ---------- Total operating income 238.4 182.0 442.4 320.7 Interest expense (12.7) (9.7) (24.0) (15.8) Interest income 3.5 2.1 6.9 6.5 Foreign currency gains (losses) (0.1) (0.4) 2.3 0.6 Other nonoperating, net (0.4) (0.1) (0.5) 0.5 ---------- ---------- ---------- ---------- Income before income taxes and minority interests 228.7 173.9 427.1 312.5 Provision for income taxes (88.3) (68.5) (165.3) (121.2) Minority interest in net income of subsidiaries (3.9) (3.5) (7.5) (6.4) ---------- ---------- ---------- ---------- Net income $ 136.5 $ 101.9 $ 254.3 $ 184.9 ========== ========== ========== ========== Basic income per share $ 0.52 $ 0.40 $ 0.97 $ 0.73 Diluted income per share $ 0.51 $ 0.40 $ 0.95 $ 0.72 Basic average common shares outstanding 262.9 253.1 262.8 252.9 Diluted average common shares outstanding 266.5 256.0 266.3 255.7 Basic and diluted per share amounts are presented in accordance with SFAS 128, "Earnings per Share".
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