Computer hangs when going from standby to hibernate

I have a problem with a laptop that often (but not always) hangs when it is
in standby mode and tries to go to hibernate mode.

There is nothing on the screen, but the status LEDs indicates, that the
machine is ON, and Caps Locks and Num Lock works. Besides from that, I can
only hold the power button to turn the machine off - and then turn it back
on. (And then it starts without any problems).

It only happens in this change - there is no problem when going directly to
hibernate mode.
There are no clues in the event viewer.

It seems like it only happens when a user is logged in, - but it happens
even if no programs are running, and I can't locate any "suspicious"
processes...

System: Fujitsu-Siemens Amilo Pro v2040 with Windows XP prof. MUI (all
updates installed).

Hope someone has a hint.

Regards

Jonathan