SHEARSON LEHMAN BROS UNIT TRUSTS HIGH YIELD TAXABLE SER 10
24F-2NT, 1999-03-30
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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 24F-2
                        Annual Notice of Securities Sold
                             Pursuant to Rule 24f-2

             Read Instructions at end of Form before preparing Form.



<TABLE>
<CAPTION>
      1.        Name and address of issuer:

                                                      Salomon Smith Barney Inc.
                                                  388 Greenwich Street, 23rd Floor
                                                         New York, NY 10013

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      2.        The name of each series or class of securities for which this Form is filed (if the Form is being filed for all
                series and classes of securities of the issuer, check the box but do not list series or classes): / /

                                                 Smith Barney Shearson Unit Trusts -
                                                    High Yield Taxable Series 10

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      3.        Investment Company Act File Number:

                                                              811-5070
                Securities Act File Number:
                                                              33-19321
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      4(a).     Last day of fiscal year for which this Form is filed:

                                                          December 31, 1998


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      4(b)./ /  Check box if this Form is being filed late (i.e., more than 90 calendar days after the end of the issuer's fiscal
                year). (See Instruction A.2)


      Note:  If the Form is being filed late, interest must be paid on the registration fee due.


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      4(c)./ /  Check box if this is the last time the issuer will be filing this Form.





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683157.1

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      5.        Calculation of registration fee:

<S>   <C>       <C>                                                                       <C>                 <C>
      (i)       Aggregate sale price of securities sold during the fiscal year
                pursuant to section 24(f):                                                                    $          0
                                                                                                              ------------

      (ii)      Aggregate price of securities redeemed or repurchased during the
                fiscal year:                                                              $ 177,883.00
                                                                                          ------------

      (iii)     Aggregate price of securities redeemed or repurchased during any
                prior fiscal year ending no earlier than October 11, 1995 that
                were not previously used to reduce registration fees payable to
                the Commission:                                                           $ 52,116.00
                                                                                          -----------

      (iv)      Total available redemption credits [add items 5(ii) and 5(iii)]:
                                                                                                              $ 229,999.00
                                                                                                              ------------
      (v)       Net sales -- if Item 5(i) is greater than Item 5(iv) [subtract
                Item 5(iv) from Item 5(i)]:                                                                   $          0
                                                                                                              ------------

      (vi)      Redemption credits available for use in future years ___ if Item
                5(i) is less than Item 5(iv) [subtract Item 5(iv) from Item
                5(i)]:                                                                    $ (229,999.00)
                                                                                          -------------

      (vii)     Multiplier for determining registration fee (See Instruction
                C.9):                                                                                         x    .000278
                                                                                                               -----------

      (viii)    Registration fee due [multiply Item 5(v) by Item 5(vii)] (enter
                "0" if no fee is due):                                                                       =$           0
                                                                                                              =============

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      6.      Prepaid Shares

      If the response to Item 5(i) was determined by deducting an amount of securities that were registered under the Securities Act
      of 1933 pursuant to rule 24e-2 as in effect before October 11, 1997, then report the amount of securities (number of shares or
      other units) deducted here: 0 . If there is a number of shares or other units that were registered pursuant to rule 24e-2
      remaining unsold at the end of the fiscal year for which this form is filed that are available for use by the issuer in future
      fiscal years, then state that number here: 0 .
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      7.      Interest due -- if this Form is being filed more than
              90 days after the end of the issuer's fiscal year  (see
              Instruction D):                                                                                +$          0
                                                                                                              ------------

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      8.      Total of the amount of the registration fee due plus
              any interest due [line 5(viii) plus line 7]:                                                   =$          0
                                                                                                              ============

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      9.      Date the registration fee and any interest payment was sent to the
              Commission's lockbox depository:

                     Method of Delivery:

                                                    / /    Wire Transfer
                                                    / /    Mail or other means

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</TABLE>


683157.1

<PAGE>



                                   SIGNATURES

      This report has been signed below by the following persons on behalf of
      the issuer and in the capacities and on the dates indicated.




      By (Signature and Title)*     /s/KEVIN KOPCZYNSKI
                                    -------------------
                                    Kevin Kopczynski
                                    First Vice President


      Date 3/25/99

  *Please print the name and title of the signing officer below the signature.

683157.1

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