STATE STREET RESEARCH EQUITY TRUST
24F-2NT, 1998-09-18
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             Annual Notice of Securities Sold Pursuant to Rule 24F-2

                                               _______________________________
          United States                        |        OMB APPROVAL          |
SECURITIES AND EXCHANGE COMMISSION             |------------------------------|
     Washington, D.C. 20549                    | OMB Number:        3235-0456 |
                                               | Expires:     August 31, 2000 |
           FORM 24F-2                          | Estimated average burden     |
Annual Notice of Securities Sold               | hours per response . . . . 1 |
      Pursuant to Rule 24f-2                   |______________________________|
                                               
   
             Read instructions at end of Form before preparing Form.

<TABLE>
<S>   <C>                                                                  <C>              <C>
- ------------------------------------------------------------------------------------------------------------------------

1.    Name and address of issuer:
         State Street Research Equity Trust
         One Financial Center
         Boston, MA 02111

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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):  [X]

- ------------------------------------------------------------------------------------------------------------------------

3.     Investment Company Act File Number:   811-4624
       Securities Act File Number:            33-4296

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4(a).  Last day of fiscal year for which this Form is filed: June 30, 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.

- ------------------------------------------------------------------------------------------------------------------------

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

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5. Calculation of registration fee:

     (i)        Aggregate sale price of securities sold during the
                fiscal year pursuant to section 24(f):                                         $596,804,488
                                                                                               ------------
     (ii)       Aggregate price of securities redeemed or
                repurchased during the fiscal year:                       $ 849,871,666
                                                                           ------------
    (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:       $           0
                                                                           ------------
<PAGE>

     (iv)       Total available redemption credits [add Items 5(ii)
                and 5(iii)]:                                                                 - $849,871,666
                                                                                               ------------
     (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      $(253,067,178)
                                                                           -----------
                --if Item 5(i) is less than Item 5(iv) 
                  [subtract Item 5(iv) from Item 5(i)]:

      (vii)     Multiplier for determining registration fee (See
                Instruction C.9):                                                            x $  1/3300
                                                                                               ------------

     (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:
       _________ 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: ___________

- ------------------------------------------------------------------------------------------------------------------------

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
                                                                                               -------------

- ------------------------------------------------------------------------------------------------------------------------

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                                        N/A

- ------------------------------------------------------------------------------------------------------------------------
</TABLE>

                                   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/ Amy L. Simmons
                           -----------------------------------------
                               Amy L. Simmons, Assistant Secretary

Date    September 18, 1998
        ------------------
*Please print the name and title of the signing officer below the signature.



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