TAX EXEMPT SECURITIES TRUST SERIES 388
S-6EL24, 1994-01-24
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  AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON JANUARY 24, 1994
						   REGISTRATION NO. 33-
==============================================================================

		      SECURITIES AND EXCHANGE COMMISSION

			   WASHINGTON, D. C. 20549
			       _______________

				   FORM S-6
			       _______________

		  FOR REGISTRATION UNDER THE SECURITIES ACT
		   OF 1933 OF SECURITIES OF UNIT INVESTMENT
		       TRUSTS REGISTERED ON FORM N-8B-2
			       _______________

A.  EXACT NAME OF TRUST:

			 TAX EXEMPT SECURITIES TRUST
				SERIES 388
			  (UNIT INVESTMENT TRUSTS)

B.  NAMES OF DEPOSITORS:

			  SMITH BARNEY SHEARSON INC.
			    KIDDER, PEABODY & CO.

C.  COMPLETE ADDRESSES OF DEPOSITORS' PRINCIPAL EXECUTIVE OFFICES:

    SMITH BARNEY SHEARSON INC.              KIDDER, PEABODY & CO.
   1345 AVENUE OF THE AMERICAS                10 HANOVER SQUARE
       NEW YORK, N.Y. 10105                  NEW YORK, N.Y. 10005



D.  NAMES AND COMPLETE ADDRESSES OF AGENTS FOR SERVICE:

    THOMAS D. HARMAN, ESQ.                    GILBERT R. OTT, JR.
     388 GREENWICH STREET                      10 HANOVER SQUARE
     NEW YORK, N.Y. 10013                     NEW YORK, N.Y. 10005


			      COPIES TO
		      PIERRE DE SAINT PHALLE, ESQ.
			 450 LEXINGTON AVENUE
			 NEW YORK, N.Y. 10017


E.  TITLE AND AMOUNT OF SECURITIES BEING REGISTERED:

 An indefinite number of Units of Beneficial Interest pursuant to Rule 24f-2
      promulgated under the Investment Company Act of 1940, as amended.


F.  PROPOSED MAXIMUM OFFERING PRICE TO THE  PUBLIC  OF  THE  SECURITIES  BEING
    REGISTERED:
				  Indefinite

G.  AMOUNT OF FILING FEE:

		       $500 (as required by Rule 24f-2)

H.  APPROXIMATE DATE OF PROPOSED SALE TO THE PUBLIC:

 As soon as practicable after the acquisition and deposit  of  the  underlying
obligations.

THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT
SHALL FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS
REGISTRATION STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH
SECTION 8(A)  OF THE SECURITIES ACT OF 1933 OR UNTIL THE REGISTRATION
STATEMENT SHALL BECOME EFFECTIVE ON SUCH DATE AS THE COMMISSION, ACTING
PURSUANT TO SAID SECTION 8(A), MAY DETERMINE.
==============================================================================


	 SUBJECT TO COMPLETION, PROSPECTUS DATED JANUARY 24, 1994



==============================================================================
						   TAX EXEMPT SECURITIES TRUST
								    SERIES 388
						      (UNIT INVESTMENT TRUSTS)
==============================================================================

     A final prospectus for a prior Series of Tax Exempt Securities Trust
is hereby incorporated by reference and used as a preliminary prospectus
for Tax Exempt Securities Trust Series 388.  Except as indicated below,
the narrative information and structure of the final prospectus for the new
Series will be substantially the same as that of the previous prospectus.
Although the previous prospectus includes the specific trusts indicated
therein, the specific trusts included in this new Series when deposited
will differ from such previous trusts.  Information with respect to the
actual trusts to be included, pricing, the size and composition of the
trust portfolios, the number of units of each trust, dates and summary
information regarding the characteristics of securities to be deposited in
the trusts of this Series is not now available and will be different from
that shown since each trust has a unique Portfolio.  Accordingly, the
information contained herein with regard to the previous Series should be
considered as being included for informational purposes only.  The
estimated current return and long-term return for the trusts of this Series
will depend on the interest rates and offering side evaluation of the
securities in each trust and may vary materially from those of the trusts
of the previous Series.  Investors should contact account executives of the
underwriters who will be informed of the expected effective date of this
Series and who will be supplied with complete information with respect to
such Series on the day of and immediately prior to the effectiveness of the
registration statement relating to Units of the trusts of this Series.

     INFORMATION CONTAINED HEREIN IS SUBJECT TO COMPLETION OR AMENDMENT.  A
REGISTRATION STATEMENT RELATING TO THESE SECURITIES HAS BEEN FILED WITH THE
SECURITIES AND EXCHANGE COMMISSION.  THESE SECURITIES MAY NOT BE SOLD NOR
MAY OFFERS TO BUY BE ACCEPTED PRIOR TO THE TIME THE REGISTRATION STATEMENT
BECOMES EFFECTIVE.  THIS PROSPECTUS SHALL NOT CONSTITUTE AN OFFER TO SELL
OR THE SOLICITATION OF AN OFFER TO BUY NOR SHALL THERE BE ANY SALE OF THESE
SECURITIES IN ANY STATE IN WHICH SUCH OFFER, SOLICITATION OR SALE WOULD BE
UNLAWFUL PRIOR TO REGISTRATION OR QUALIFICATION UNDER THE SECURITIES LAWS
OF ANY SUCH STATE.



				   PART II

	    ADDITIONAL INFORMATION NOT INCLUDED IN THE PROSPECTUS

     A.  The following information relating to the Depositors is
incorporated by reference to the SEC filings indicated and made a part of
this Registration Statement.
							      SEC FILE OR
							   IDENTIFICATION NO.
							   __________________

I.  Bonding Arrangements and Date of Organization of the Depositors filed
    pursuant to Items A and B of Part II of the Registration Statement on
    Form S-6 under the Securities Act of 1933:

	 Smith Barney Shearson Inc.                               2-55436
	 Kidder, Peabody & Co. Incorporated

II. Information as to Officers and Directors of the Depositors filed
    pursuant to Schedules A and D of Form BD under Rules 15b1-1 and 15b3-1
    of the Securities Exchange Act of 1934:

	 Smith Barney Shearson Inc.                                8-8177
	 Kidder, Peabody & Co. Incorporated                        8-4831


III. Charter documents of the Depositors filed as Exhibits to the
     Registration Statement on Form S-6 under the Securities Act of 1933
     (Charter, By-Laws):

	 Smith Barney Shearson Inc.                    33-65332, 33-36037
	 Kidder, Peabody & Co. Incorporated            33-17979, 33-20499

     B.  The Internal Revenue Service Employer Identification Numbers of
the Sponsors and Trustee are as follows:
.\"the Sponsors and Co-Trustees are as follows:

	 Smith Barney Shearson Inc.                            13-1912900
	 Kidder, Peabody & Co. Incorporated                    13-5650440
	 United States Trust Company of New York, Trustee      13-5459866

				     II-1



Supplemented final prospectuses from the following Series of Tax Exempt
Securities Trust (all of which are incorporated herein by reference) may be
used as preliminary prospectuses for this Series:  Tax Exempt Securities
Trust, Series 379 (Reg.  No. 33-49999);  Tax Exempt Securities Trust,
Series 380 (Reg.  No. 33-50001);  Tax Exempt Securities Trust, Series 381
(Reg.  No. 33-50365);  Tax Exempt Securities Trust, Series 382 (Reg.  No.
33-50367);  Tax Exempt  Securities  Trust,  Series 383 (Reg.  No.
33-50917); Tax Exempt Securities Trust, Series 384 (Reg.  No. 33-50915);
Tax Exempt Securities Trust Series 385 (Reg.  No.   33-51397).


		    CONTENTS OF REGISTRATION STATEMENT

 THE REGISTRATION STATEMENT ON FORM S-6 COMPRISES THE FOLLOWING PAPERS AND
DOCUMENTS:

 The facing sheet of Form S-6.
 The Cross-Reference Sheet (incorporated by reference to the Cross-
   Reference Sheet to the Registration Statement of Tax Exempt Securities
   Trust, Series 384, 1933 Act File No. 33-50915).
 The Prospectus.
 Additional Information not included in the Prospectus (Part II).
 *Consent of independent public accountants.

 The following exhibits:

      1.1       --  Form of Trust Indenture and Agreement (incorporated
		    by reference to Exhibit 4.a to the Registration
		    Statement of Tax Exempt Securities Trust, Series 265,
		    1933 Act File No. 33-15123).

      1.1.1      -- Form of Reference Agreement Trust (incorporated by
		    reference to Exhibit 4.b to the Registration Statement
		    of Tax Exempt Securities Trust, Series 384, 1993 Act
		    File No. 33-50915).

      1.2       --  Form of Agreement Among Underwriters (incorporated
		    by reference to Exhibit 99 to the Registration
		    Statement of Tax Exempt Securities Trust, Series 384,
		    1933 Act File No. 33-50915).

      2.1       --  Form of Certificate of Beneficial Interest (included in
		    Exhibit 1.1).

     *3.1       --  Opinion of counsel as to the legality of the securities
		    being issued including their consent to the use of
		    their names under the headings "Taxes" and
		    "Legal Opinion" in the Prospectus.

     *4.1       --  Consent of the Evaluator


__________

  * To be filed with Amendment to Registration Statement.


				     II-2


				  SIGNATURES

     PURSUANT TO THE REQUIREMENTS OF THE SECURITIES ACT OF 1933, THE
REGISTRANT HAS DULY CAUSED THIS REGISTRATION STATEMENT OR AMENDMENT TO THE
REGISTRATION STATEMENT TO BE SIGNED ON ITS BEHALF BY THE UNDERSIGNED
THEREUNTO DULY AUTHORIZED IN THE CITY OF NEW YORK AND STATE OF NEW YORK
ON THE 24TH DAY OF JANUARY, 1994.


	    Signatures appear on pages II-4 and II-5.

     A majority of the members of the Board of Directors of Smith Barney
Shearson Inc. has signed this Registration Statement or Amendment to the
Registration Statement pursuant to Powers of Attorney authorizing the
person signing this Registration Statement or Amendment to the Registration
Statement to do so on behalf of such members.

     A majority of the members of the Board of Directors of Kidder, Peabody
& Co. Incorporated has signed this Registration Statement or Amendment to
the Registration Statement pursuant to Powers of Attorney authorizing the
person signing this Registration Statement or Amendment to the Registration
Statement to do so on behalf of such members.



				     II-3


   SMITH BARNEY SHEARSON INC.
	  DEPOSITOR


   By the following persons*,             *Pursuant to Powers of Attorney
      who constitute a majority of           filed under the 1933 Act
      the Board of Directors of              File Number 33-56722.
      Smith Barney Shearson Inc.:


       RONALD A. ARTINIAN
       STEVEN D. BLACK
       JAMES DIMON
       ROBERT DRUSKIN
       TONI ELLIOTT
       LEWIS GLUCKSMAN
       THOMAS GUBA
       JOHN B. HOFFMAN
       A. RICHARD JANIAK, JR.
       ROBERT Q. JONES
       JEFFREY LANE
       JACK H. LEHMAN III
       JOEL N. LEVY
       HOWARD D. MARSH
       WILLIAM J. MILLS II
       JOHN C. MORRIS
       A. GEORGE SAKS
       BRUCE D. SARGENT
       MELVIN B. TAUB
       JACQUES S. THERIOT
       STEPHEN J. TREADWAY
       PAUL UNDERWOOD



       By  GEORGE S. MICHINARD, JR.
	  (As authorized signatory for
	  Smith Barney Shearson Inc. and
	  Attorney-in-fact for the persons listed above)


				     II-4

   KIDDER, PEABODY & CO. INCORPORATED,
      DEPOSITOR



   By the following persons*, who             *Pursuant to Powers of Attorney
      constitute a majority of the               filed under the 1933 Act
      Board of Directors of                      File Number 33-37951.
      Kidder, Peabody & Co. Incorporated:


	      MICHAEL A. M. KEEHNER
	      JOHN M. LIFTIN
	      JAMES A. MULLIN
	      RICHARD W. O'DONNELL
	      THOMAS F. RYAN, JR.


	      By GILBERT R. OTT, JR.
		 (As authorized signatory for
		 Kidder, Peabody & Co. Incorporated and
		 Attorney-in-fact for the persons listed above)


				     II-5



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