Filing Pursuant to Rule 424(b)(3)
                                            Registration Statement No. 333-48536

                PROSPECTUS SUPPLEMENT NO. 13 DATED JUNE 4, 2001
                      TO PROSPECTUS DATED JANUARY 22, 2001

                      TERAYON COMMUNICATION SYSTEMS, INC.

                                  $500,000,000

     of 5% Convertible Subordinated Notes Due 2007 and 5,951,673 Shares of
               Common Stock Issuable Upon Conversion of the Notes

Please read this prospectus supplement in conjunction with the prospectus dated
January 22, 2001 (the "Prospectus"). The table on pages 21 thru 24 of the
Prospectus setting forth information concerning the selling holders, prospectus
supplement no. 1 dated February 9, 2001, prospectus supplement no. 2 dated
February 16, 2001, prospectus supplement no. 3 dated February 20, 2001,
prospectus supplement no. 4 dated February 23, 2001, prospectus supplement no. 5
dated March 2, 2001, prospectus supplement no. 6 dated March 9, 2001, prospectus
supplement no. 7 dated March 16, 2001, prospectus supplement no. 8 dated March
23, 2001, prospectus supplement no. 9 April 27, 2001, prospectus supplement no.
10 dated May 4, 2001, prospectus supplement no. 11 dated May 11, 2001 and
prospectus supplement no. 12 dated May 25, 2001 are superseded by the following
table:

                                SELLING HOLDERS

We originally issued the Notes and the Notes were sold by the initial purchasers
in a transaction exempt from the registration requirements of the Securities Act
to persons reasonably believed by the initial purchasers to be qualified
institutional buyers or other institutional accredited investors.  Selling
holders, including their transferees, pledgees or donees or their successors,
may from time to time offer and sell pursuant to this prospectus any or all of
the Notes and common stock into which the Notes are convertible.  We agreed to
use reasonable efforts to keep the registration statement effective until July
26, 2002.  Our registration of the Notes and the shares of common stock into
which the Notes are convertible does not necessarily mean that the selling
holders will sell any or all of the Notes or the shares of the common stock into
which the Notes are convertible.

The following table sets forth information, as of June 4, 2001, with respect to
the selling holders and the principal amounts of Notes beneficially owned by
each selling holder that may be offered under this prospectus.  The information
is based on information provided by or on behalf of the selling holders.  The
selling holders may offer all, some or none of the Notes or common stock into
which the Notes are convertible.  Because the selling holders may offer all or
some portion of the Notes or the common stock, no estimate can be given as to
the amount of the Notes or the common stock that will be held by the selling
holders upon termination of any sales.  In addition, the selling holders
identified below may have sold, transferred or otherwise disposed of all or a
portion of their Notes since the date on which they provided the information
regarding their Notes in transactions exempt from the registration requirements
of the Securities Act.



                                                                Principal Amount     Common Stock
                                                                    of Notes        Issuable upon
                                                               Beneficially Owned     Conversion         Common
                       Selling Holder                             and Offered        of the Notes     Stock Offered
                       --------------                          ------------------  ----------------  ---------------
                                                                                            
Arbitex Master Fund, L.P.                                               1,200,000            14,284           14,284

Aventis Pension Master Trust                                              440,000             5,237            5,237


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                                                                Principal Amount     Common Stock
                                                                    of Notes        Issuable upon
                                                               Beneficially Owned     Conversion         Common
                       Selling Holder                             and Offered        of the Notes     Stock Offered
                       ------------                            ------------------  ----------------  ---------------
                                                                                            
Black Diamond Offshore, Ltd.                                              665,000             7,915            7,915

Boilermaker - Blacksmith Pension Trust                                  2,700,000            32,139           32,139

BS Debt Income Fund - Class A                                              15,000               178              178

CALAMOS(R) Convertible Portfolio - CALAMOS(R) Advisors Trust              150,000             1,785            1,785

CALAMOS(R) Convertible Technology - Fund  CALAMOS(R)
 Investment Trust                                                         230,000             2,737            2,737

CALAMOS(R) High Yield Fund - CALAMOS(R) Investment Trust                  245,000             2,916            2,916

City of Albany Pension Fund                                               245,000             2,916            2,916

City of Knoxville Pension System                                          640,000             7,618            7,618

Credit Suisse First Boston                                              1,000,000            11,903           11,903

Delta Airlines Master Trust                                             4,900,000            58,326           58,326

Delta Pilots Disability Survivorship Trust                                200,000             2,380            2,380

Deutsche Bank Securities Inc.                                             200,000             2,380            2,380

Double Black Diamond Offshore, LDC                                      2,708,000            32,234           32,234

ECT Investments, Inc.                                                   1,000,000            11,903           11,903

Greenlight Capital, L.P.                                                1,055,000            12,558           12,558

Greenlight Capital Offshore, Ltd.                                       2,413,000            28,722           28,722

Greenlight Capital Qualified, L.P.                                      2,532,000            30,139           30,139

Ilanot Batucha Investment House, Ltd.                                     300,000             3,571            3,571

Israel Brokerage & Investments IBI, Ltd.                                  100,000             1,190            1,190

Jefferies & Co.                                                           875,000            10,415           10,415

JMG Capital Partners, L.P.                                                500,000             5,951            5,951


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                                                                Principal Amount     Common Stock
                                                                    of Notes        Issuable upon
                                                               Beneficially Owned     Conversion         Common
                       Selling Holder                             and Offered        of the Notes     Stock Offered
                       --------------                          ------------------  ----------------  ---------------
                                                                                            
JMG Triton Offshore Fund, Ltd.                                            500,000             5,951            5,951

JRS, Ltd.                                                               1,000,000            11,903           11,903

Julius Baer Securities, Inc.                                              250,000             2,975            2,975

KBC Financial Products USA, Inc.                                          900,000            10,713           10,713

Kettering Medical Center Funded-Depreciation Account                      160,000             1,904            1,904

Knoxville Utilities Board Retirement System                               400,000             4,761            4,761

Lehman Brothers, Inc.                                                   1,200,000            14,284           14,284

Leonardo, L.P.                                                         12,000,000           142,840          142,840

LibertyView Funds, L.L.C.                                                 100,000             1,190            1,190

LibertyView Funds, L.P.                                                   400,000             4,761            4,761

Lonestar Partners, L.P.                                                 4,500,000            53,565           53,565

Louisiana Workers' Compensation Corporation                               360,000             4,285            4,285

Lumber Industries, Inc.                                                   750,000             8,927            8,927

Lydian Overseas Partners Master Fund                                   15,000,000           178,550          178,550

McMahan Securities Co., L.P.                                            1,000,000            11,903           11,903

Merrill, Lynch, Pierce, Fenner and Smith, Inc.                             16,000               190              190

Morgan Stanley & Co.                                                    2,500,000            29,758           29,758

Pacific Life Insurance Company                                          1,000,000            11,903           11,903

Port Authority of Allegheny County Retirement and Disability
 Allowance Plan for the Employees Represented by Local 85 of
 the Amalgamated Transit Union                                          2,825,000            33,626           33,626

Ramus Capital Group Holdings, Ltd.                                        200,000             2,380            2,380

Research Capital Corporation                                              750,000             8,927            8,927

Spear, Leads & Kellogg Capital Markets                                  2,400,000            28,568           28,568

SPT                                                                     1,100,000            13,093           13,093


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                                                                Principal Amount     Common Stock
                                                                    of Notes        Issuable upon
                                                               Beneficially Owned     Conversion         Common
                       Selling Holder                             and Offered        of the Notes     Stock Offered
                       --------------                          ------------------  ----------------  ---------------
                                                                                            
Standard Mortgage Holding Corp.                                           500,000             5,951            5,951

The Class IC Company, Ltd.                                              1,500,000            17,855           17,855

The Dow Chemical Company Employees' Retirement Plan                     5,325,000            63,385           63,385

The Fondren Foundation                                                    165,000             1,964            1,964

Unifi, Inc. Profit Sharing Plan and Trust                                 255,000             3,035            3,035

United Food and Commercial Workers Local 1262 and Employees
 Pension Fund                                                           1,260,000            14,998           14,998

United Mizrahi Bank, Ltd.                                                  50,000               595              595

Valentis Investors, L.L.C.                                              2,000,000            23,806           23,806

Van Waters & Rogers, Inc. Retirement Plan                                 770,000             9,165            9,165

Any other holders of Notes or future holders (3)                      414,551,000         4,934,565        4,934,565

Total                                                                 500,000,000         5,951,673        5,951,673

(1)  Assumes a conversion rate of 11.9033 shares of common stock per $1,000
     principal amount of Notes and a cash payment in lieu of any fractional
     interest.

(2)  Assumes that any other holders of Notes or any future transferee from any
     holder do not or will not beneficially own any common stock other than
     common stock into which the Notes are convertible at the conversion rate of
     11.9033 shares of common stock per $1,000 principal amount of Notes.

(3)  The principal amount of Notes held by other holders or future holders
     includes $195,597,000 principal amount of Notes repurchased by the Company
     in February 2001 which is convertible into 2,328,258 shares of common
     stock.

None of the selling holders nor any of their affiliates, officers, directors or
principal equity holders has held any position or office or has had any material
relationship with us within the past three years with the exception of Deutsche
Bank Securities, Inc. and Lehman Brothers, Inc. In the past three years,
Deutsche Bank, Inc. and Lehman Brothers, Inc. have acted as underwriters of the
Company's initial public offering and follow-on public offering and were initial
purchasers in the offering of the Notes.  The selling holders purchased all of
the Notes in a private transaction.  All of the Notes and the shares of common
stock into which the Notes are convertible are "restricted securities" under the
Securities Act.

Information concerning the selling holders may change from time to time and any
changed information will be set forth in supplements to this prospectus if and
when necessary.  In addition, the conversion price, and therefore, the number of
shares of common stock issuable upon conversion of the Notes, is subject to
adjustment under certain circumstances.  Accordingly, the aggregate principal
amount of Notes and the number of shares of common stock into which the Notes
are convertible may increase or decrease.

            The date of this Prospectus Supplement is June 4, 2001.

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