U.S. SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C. 20549


                                  FORM 24F-2
                       ANNUAL NOTICE OF SECURITIES SOLD
                             PURSUANT TO RULE 24f-2


           READ INSTRUCTIONS AS END OF FORM BEFORE PREPARING FORM.
                             PLEASE PRINT OR TYPE.

 ______________________________________________________________________________
 1. Name and address of issuer:


         Piper Funds Inc. -- II

 ______________________________________________________________________________
 2. Name of each series or class of funds for which this notice is filed:
 
 
         Adjustable Rate Mortgage Securities Fund

 ______________________________________________________________________________
 3. Investment Company Act File Number: 
 
                                811-07279
    Securities Act File Number: 33-67016
 ______________________________________________________________________________
 4. Last day of fiscal year for which this notice is filed:

         August 31, 1996

 ______________________________________________________________________________
 5. Check box if this notice is being filed more than 180 days after the close
    of the issuer's fiscal year for purposes of reporting securities sold 
    after the close of the fiscal year but before termination of the issuer's
    24f-2 declaration:

                                                                         / /
 ______________________________________________________________________________
 6. Date of termination of issuer's declaration under rule 24f-2(a)(1), if
    applicable (see instruction A.6): 


         n/a

 ______________________________________________________________________________
 7. Number and amount of securities of the same class or series which had been
    registered under the Securities Act of 1933 other than pursuant to rule
    24f-2 in a prior fiscal year, but which remained unsold at the beginning
    of the fiscal year: 


         n/a

 ______________________________________________________________________________
 8. Number and amount of securities registered during the fiscal year other 
    than pursuant to rule 24f-2:



         0
 ______________________________________________________________________________
 9. Number and aggregate sale price of securities sold during the fiscal 
    year: 


         151,839,032.313 shares; $1,364,419,622.20

  _____________________________________________________________________________


 ______________________________________________________________________________
 10. Number and aggregate sale price of securities sold during the fiscal 
     year in reliance upon registration pursuant to rule 24f-2.


         151,839,032.313 shares; $1,364,419,622.20

 ______________________________________________________________________________

 11. Number and aggregate sale price of securities issued during the fiscal 
     year in connection with dividend reinvestment plans, if applicable (see 
     instruction B.7):


         1,638,150.407 shares; $13,155,272.70

 ______________________________________________________________________________

 12. Calculation of registration fee:

     (i) Aggregate sale price of securities sold during     + $1,364,419,622.20
         the fiscal year in reliance on rule 24f-2          ___________________
         (from Item 10):
    (ii) Aggregate price of shares issued in connection     +  13,155,272.70
         with dividend reinvestment plans (from Item 11,    ___________________
         if applicable):
   (iii) Aggregate price of shares redeemed or repurchased  - 960,709,462.92
         during the fiscal year (if applicable):            ___________________
    (iv) Aggregate price of shares redeemed or repurchased  +        0
         and previously applied as a reduction to filing    ___________________
         fees pursuant to rule 24e-2 (if applicable):
     (v) Net aggregate price of securities sold and issued    416,865,431.98
         during the fiscal year in reliance on rule 24f-2   ___________________
         line (i), plus line (ii), less line (iii), plus
         line (iv) (if applicable):
    (vi) Multiplier prescribed by Section 8(b) of the       x 0.0003030303 or 
         Securities Act of 1933 or other applicable law or    1/33 of 1%
         regulation (see instruction C.8):                  ___________________
   (vii) Fee due (line (i) or line (v) multiplied by          $126,322.86
         line (vi)):                                        ___________________

 INSTRUCTION: ISSUERS SHOULD COMPLETE LINES (ii), (iii), (iv), AND (v) ONLY IF
               THE FORM IS BEING FILED WITHIN 60 DAYS AFTER THE CLOSE OF THE 
               ISSUER'S FISCAL YEAR. See Instruction C.3.
_______________________________________________________________________________
 13. Check box if fees are being remitted to the Commission's lockbox 
     depository as described in Section 3a of the Commission's Rules of
     Informal and Other Procedures (17 CFR 202.3a).

                                                                         / /

     Date of mailing or wire transfer of filing fees to the Commission's
     lockbox depository:

                               October 24, 1996

_______________________________________________________________________________
                                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)* Robert H. Nelson
                           _______________________________________________
                            Vice President and Treasurer
                           _______________________________________________


  Date________________________

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