The following thread is closed: 133552-howto-linux-multihomed-dns-client (Sorry I am not allowed to post URLs)
Therefore I write this append in an own thread.
The HOWTO in the referenced thread helped me a lot and I only want to append how to make reverse lookup working for a local zone:
One had to add the following lines:
zone "1.1.10.in-addr.arpa" { // the reversed cluster of your local network
type forward;
forwarders {
w.x.y.z; // your private name server
};
};