More info:
I select the 'rig-controller' at time O and key.
I move the character to time at time 10, and key again.
The WHOLE character animates! Yeah! ;-)

At time 10, I move one controller of the rigg (arm) and key that position of the arm.
But when I go back in time to time O, the arm stays in the position I keyed at time 10.

So not all attributes are keyed at time 0 when I set key at that time.

Please advice! Thx!