I found the problem - it was a plugin that caused the problem. I ran cron manually and found an error. Unfortunately I didn't make a print screen and I don't want to install the plugin again.
So I need to find out when I have more time how plugins really work. Where you could run into problems. I found out that the plugin created a record in mdl_config_plugins, mdl_modules and mdl_course_moduls. I have to do more investigations.
Thanks, Rainer