UNITED STATES SECURITIES AND EXCHANGE COMMISSION
WASHINGTON, D.C. 20549
FORM 4
STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP
( ) Check this box if no longer subject to Section 16.
Form 4 or Form 5 obligations may continue. See Instructions 1(b).
1. Name and Address of Reporting Person
   BACIOCCO, ALBERT J., Jr.
   
   747 Pitt Street
   Mt. Pleasant, SC  29464
2. Issuer Name and Ticker or Trading Symbol
   Honeywell Inc.
   HON
3. IRS or Social Security Number of Reporting Person (Voluntary)
   
4. Statement for Month/Year
   06/1998
5. If Amendment, Date of Original (Month/Year)
   
6. Relationship of Reporting Person(s) to Issuer (Check all applicable)
   (X) Director ( ) 10% Owner ( ) Officer (give title below) ( ) Other
   (specify below)
   
7. Individual or Joint/Group Filing (Check Applicable Line)
   (X) Form filed by One Reporting Person
   ( ) Form filed by More than One Reporting Person


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 Table I -- Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned                                                 |
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1. Title of Security       |2.    |3.    |4.Securities Acquired (A)         |5.Amount of        |6.Dir |7.Nature of Indirect       |
                           | Transaction |  or Disposed of (D)              |  Securities       |ect   |  Beneficial Ownership     |
                           |      |      |                                  |  Beneficially     |(D)or |                           |
                           |      |    | |                  | A/|           |  Owned at         |Indir |                           |
                           | Date |Code|V|    Amount        | D |    Price  |  End of Month     |ect(I)|                           |
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Common Stock               |06/15/|J*  |V|2.7442            |A  |N/A        |2,286              |D     |                           |
                           |98    |    | |                  |   |           |                   |      |                           |
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 Table II -- Derivative Securitites Acquired, Disposed of, or Beneficially Owned                                                   |
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1.Title of Derivative |2.Con-  |3.   |4.    |5.Number of De |6.Date Exer|7.Title and Amount  |8.Price|9.Number    |10.|11.Nature of|
  Security            |version |Transaction | rivative Secu |cisable and|  of Underlying     |of Deri|of Deriva   |Dir|Indirect    |
                      |or Exer |     |      | rities Acqui  |Expiration |  Securities        |vative |tive        |ect|Beneficial  |
                      |cise    |     |      | red(A) or Dis |Date(Month/|                    |Secu   |Securities  |(D)|Ownership   |
                      |Price of|     |      | posed of(D)   |Day/Year)  |                    |rity   |Benefi      |or |            |
                      |Deriva- |     |      |               |Date |Expir|                    |       |ficially    |Ind|            |
                      |tive    |     |      |           | A/|Exer-|ation|   Title and Number |       |Owned at    |ire|            |
                      |Secu-   |     |    | |           | D |cisa-|Date |   of Shares        |       |End of      |ct |            |
                      |rity    |Date |Code|V|  Amount   |   |ble  |     |                    |       |Month       |(I)|            |
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Phantom Stock Units   |1-for-1 |06/15|A** |V|44.5551    |A  |***  |***  |Common Stock|44.5551|$83.468|            |   |            |
                      |        |/98  |    | |           |   |     |     |            |       |7      |            |   |            |
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Phantom Stock Units   |1-for-1 |06/30|A   |V|63.8693    |A  |***  |***  |Common Stock|63.8693|$82.668|13,390.4239 |D  |            |
                      |        |/98  |    | |           |   |     |     |            |       |7      |            |   |            |
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                      |        |     |    | |           |   |     |     |            |       |       |            |   |            |
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Explanation of Responses:
* These shares were acquired under the Honeywell Dividend Reinvestment 
Plan.
** Dividend equivalent rights accrued and converted to phantom stock units 
under Honeywell's Non-Employee 
Directors Fee and Stock Unit 
Plan.
***Stock units were accrued under Honeywell's Non-Employee Directors Fee and 
Stock Unit Plan and will settle 
when Reporting Person's service as a Director 
terminates.
SIGNATURE OF REPORTING PERSON
Kathleen M. Gibson on behalf of Albert J. Baciocco
DATE
July 9, 1998