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): May 20, 1998

                                AlliedSignal Inc.
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             (Exact name of registrant as specified in its charter)

         Delaware                      1-8974                   22-2640650
      --------------                ------------              --------------
     (State or other                (Commission             (I.R.S. Employer
     jurisdiction of                File Number)            Identification No.)
     incorporation)

             101 Columbia Road
              P.O. Box 4000
          Morristown, New Jersey                                 07962-2497
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     (Address of principal executive offices)                    (Zip Code)

     Registrant's telephone number, including area code:  (973) 455-2000

Item 5.  Other Events.
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The Registrant issued on May 20, 1998 the following press release:

                    AlliedSignal Offers To Exchange New Debt
                      For $450 Million Of Outstanding Debt

     MORRIS TOWNSHIP, New Jersey, May 20, 1998 - AlliedSignal Inc. (NYSE:ALD)
today announced that it will offer to exchange new longer-maturity debentures
for certain of its outstanding debentures.

     AlliedSignal will offer to exchange debentures due June 1, 2033 for its
outstanding $100,000,000 principal amount of 9 1/2% debentures due June 1,
2016. In addition, AlliedSignal will offer to exchange notes due July 1, 2005
for its outstanding $250,000,000 principal amount of 9 7/8% debentures due June
1, 2002 and its outstanding $100,000,000 principal amount of 9.20% debentures
due February 15, 2003. The exchange offers are being made to holders of the
outstanding debentures pursuant to an exemption from registration under Section
3(a)(9) of the Securities Act of 1933.

     The exchange offers expire on June 18, 1998, unless extended by
AlliedSignal.

     The exchange offers are being made by offering circular. Holders of the
above-listed debentures may call Georgeson & Company Inc. at (800) 223-2064 for
further information about the offer.

     AlliedSignal is an advanced technology and manufacturing company serving
customers worldwide with aerospace and automotive products, chemicals, fibers,
plastics and advanced materials. Additional information on the company is
available on the World Wide Web at http://www.alliedsignal.com/.

                                   SIGNATURES
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     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.

                                  AlliedSignal Inc.
                                  (Registrant)

Date: May 20, 1998           By: /s/ Peter M. Kreindler
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                                Peter M. Kreindler
                                Senior Vice President,
                                General Counsel and Secretary