Meanwhile, I found the reason:
DNS queries are performed using IPv6 only on my machines, ignoring the IPv4 settings which also is activated. In the netcard settings for this protocol, "Automatic" was selected, but in the Extended dialog's DNS tab, a DNS server address was missing on those machines which exposed the problem. After entering a server address, everything works fine now.



Note as a takeaway: The DNS settings for IPv4 apparently don't work anymore, at least when IPv6 is activated.