Hi Brian, as promised, I want to report my last experiences. The problem with the delay on both of my notebooks is solved.
Due to your help, I could figured out, that the process network-manager caused the delay. This happened, because the purge of the package was not completed, so that binary files and some config files stayed on the system. New installation and then deinstallation with purge did the trick. A similar problem was with my EEEPC. In this case, the package ntpdate searched for an IP 192.168.178.1 (which is my fritzbox), and did not find it. Of course it cannot find it, because I am behind another router, with the IP range 192.168.1.*. However, in none of the configuration files of ntpdate the IP 192.168.178.1 appeared! As ntpdate is not necessary and is fully successed through the package ntp, I deinstalled and purged ntpdate and everything was working again. Thank you for pointing me to the systemctrl commands, so I could see, learn and solve the problem. Best Hans