After all I managed Knoppix to accept the stick.
The problem was obviously in the filesystem.
I didn't bother investigating much - I just found a post somwhere on the Internet saying that sticks can be formatted in some 'superfloppy' standard and that Linux may have problems with that.
I had to use another distribution (SLAX) to repartition the stick. It had to be formatted afterwards. Then it worked well both under Windows and Linux.

It is just a pity that Knoppix hangs completely. SLAX just said it could not be mounted, but allowed partitioning with 'fdisk'.