This is the MySQL-Log-File:

 060126  8:04:15  InnoDB: Started; log sequence number 0 43655
 060126  8:04:16 [Note] D:\MyProject\mysql\bin\mysqld-nt.exe: ready
for connections.
 Version: '5.0.18-nt'  socket: ''  port: 3306  MySQL Community Edition
(GPL)
 060126  8:04:50 [Note] D:\MyProject\mysql\bin\mysqld-nt.exe: Normal
shutdown

 060126  8:04:50  InnoDB: Starting shutdown...
 060126  8:04:54  InnoDB: Shutdown completed; log sequence number 0
43655
 060126  8:04:54 [Note] D:\MyProject\mysql\bin\mysqld-nt.exe: Shutdown
complete

This logs tells me that the db was ready for connections 1 second after
it was started.
(What is InnoDB?).

But the log of my program says that it took 20 seconds:

 08:03:54 - starting database:
   "C:\mysql\bin\mysqld-nt.exe" "--basedir=C:\mysql" --standalone
--port=3306 --max_allowed_packet=128M
 08:03:54 - connecting to database:
   URL=jdbc:mysql://localhost:3306/trigonis
   user=root
   ..............
 08:04:16 - connection succeeded:
   dbms=MySQL 5.0.18-nt
   driver=MySQL-AB JDBC Driver mysql-connector-java-3.1.12 ( $Date:
2005-11-17 15:53:48 +0100 (Thu, 17 Nov 2005) $, $Revision$ )

I start mysqld-nt.exe using the ProcessBuilder class. Then I try to
connect. Whenever the connection fails I print a dot and sleep for 500
milliseconds.

I also tried to create a socket for port 3306. That fails too if I try
do create it within the first 20 to 30 seconds after starting the
process.

This happens only on some machines. On other machines the time between
starting the process and a successful connection is less than a second.
With MySQL 3.25 everything worked fine on all machines. All machines
are identical. The users' profiles may differ.