<PAGE>

                                                                   EXHIBIT 10.19

                AMENDED AND RESTATED MARKET STAND-OFF AGREEMENT


     This Market Stand-Off Agreement (the "Agreement") is effective as of June
19, 1998 (the "Effective Date") between ALZA Corporation, a Delaware corporation
               --------------
("ALZA") and Durect Corporation ("Durect").
  ----                            ------

                                    RECITALS
                                    --------

     A.   ALZA and Durect are parties to that certain Amended and Restated
Development and Commercialization Agreement dated April 28, 1999 (the "DUROS
                                                                       -----
Agreement"), providing for the development, manufacture and marketing of
---------
pharmaceutical products utilizing proprietary technology of ALZA relating to the
DUROS(R) System for the controlled delivery of drugs in certain fields.

     B.   In consideration for a worldwide, royalty free, nonexclusive license,
with the right to grant sublicenses, to any Technical Information (as defined in
the DUROS Agreement) that Durect develops relating to a means of connecting or
"docking" a catheter to a System (as defined in the DUROS Agreement) granted to
ALZA pursuant to the last sentence of Section 8.1 of the DUROS Agreement (the
"Docking License"), ALZA is willing to agree to certain restrictions on the
transferability of any securities of Durect that ALZA currently owns or expects
to own.

     C.   The parties wish to set forth the terms of such restriction and to
enter into this Agreement.

     NOW, THEREFORE, the parties hereby agree as follows:

     1.   Definitions.  Unless otherwise defined herein, all capitalized terms
          -----------
shall have the same defined meanings as in the DUROS Agreement.

     2.   Covenants of ALZA.
          -----------------

          2.1  "Market Stand-Off" Agreement.  ALZA hereby agrees that, during
               ----------------------------
the period (the "Lock-Up Period") that is two years after the termination of any
                 --------------
market stand-off or similar agreement that ALZA enters into with Durect or with
any underwriter of Common Stock or other securities of Durect in connection with
Durect's initial public offering of Common Stock (the "IPO"), ALZA (or any
                                                       ---
affiliated entity or person of ALZA) shall not, during any six month period,
directly or indirectly sell, offer to sell, contract to sell (including, without
limitation, any short sale), pledge, grant any option to purchase or otherwise
transfer or dispose of twenty five percent (25%) or more of the maximum number
of all securities of Durect held by ALZA (and any affiliated entity or person of
ALZA) at any given time during the period commencing on the date of the Series
A-1 Closing (as defined in the Series A-1 and Series A-2 Preferred Stock
Purchase Agreement dated June 19, 1998) and ending on the  closing of the IPO;
provided, however, that such restrictions shall not apply to any conversion of
Durect securities held by ALZA, or to any transfer of Durect securities by ALZA
in connection with a merger, exchange offer or other transaction affecting
Durect shareholders generally.
<PAGE>

          To the extent necessary in order to enforce the foregoing covenant,
Durect may impose stop-transfer instructions with respect to the securities held
by ALZA until the end of the Lock-Up Period.  Durect shall provide appropriate
releases to such stop transfer instructions for transactions in compliance with
this Agreement within two business days of ALZA's request therefor.

          2.2  Termination of Docking License.  ALZA hereby agrees that, in the
               -------------------------------
event that it or any of its affiliated entities or persons shall violate the
covenant in Section 2.1 of this Agreement, ALZA and its affiliates shall forfeit
any and all rights under the Docking License and such Docking License shall
terminate as of the time that the covenant in Section 1.1 of this Agreement is
first violated without any further action on the part of Durect.

     3.   Miscellaneous.
          -------------

          3.1  Controlling Law; Language.  This Agreement and the performance of
               -------------------------
the parties hereunder shall be construed in accordance with and be governed by
the laws of the State of California, as applied to agreements between California
residents to be performed entirely within California.

          3.2  Successors and Assigns.  The provisions of this Agreement shall
               ----------------------
inure to the benefit of, and be binding upon, the successor and assigns of the
parties hereto.

          3.3  Amendments and Waivers.  Neither this Agreement nor any term of
               ----------------------
this Agreement may be amended, waived or terminated other than by the written
consent of the party against whom enforcement of any such amendment, waiver or
termination is sought.

          3.4  Severability.  If one or more provisions of this Agreement are
               ------------
held to be unenforceable under applicable law, the parties agree to renegotiate
such provision in good faith.  In the event that the parties cannot reach a
mutually agreeable and enforceable replacement for such provision, then (a) such
provision shall be excluded from this Agreement, (b) the balance of the
Agreement shall be interpreted as if such provision were so excluded and (c) the
balance of the Agreement shall be enforceable in accordance with its terms.

          3.5  Counterparts.  This Agreement may be executed in two or more
               ------------
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

                            [Signature Page Follows]
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have hereby caused this Agreement to
be executed as of the date first written above by their duly authorized
representatives.

ALZA CORPORATION                         DURECT CORPORATION


By: /s/ Peter Staples                    By: /s/ James E. Brown
   --------------------------------         ------------------------------------


Title: Executive Vice President          Title: Chief Executive Officer
      -----------------------------            ---------------------------------


                 SIGNATURE PAGE TO MARKET STAND-OFF AGREEMENT