And my problem is:
Only registered users should be able to download then files. Is it possible to do that?

Because: if the file is uploaded on the server, then anybody who know the URL can download it.
One workaround is not to upload the file to server directory, but rather to store the file in the MySQL database. But I seek for some easier way (or plugin).

Thanx for any hint

Yes it is true that once a file is on a website that anyone with the URL can download it, but there are some significant practical limitations you can impose:
– they must know the full name
– they must get past any access rules in your “.htaccess” file