How to foward subdomains?

[Sdävtaker]

Hello
Sorry in advance for my english,it is not my main language.
I got a tiny network with 2 computers and only 1 external ip.
I configured my router to foward the dns port to machine1, and
registered it in nic as ns1.mydomain.com, i had successfully moved my
registered domains to that dns and could run all my services in that
machine, ie i can http://www.mydomain.com from outside.
After that i had setup a second machine in the network and i want to
make this one a subdomain of the first one ie second.mydomain.com,
this second machine got no external ip.
How can i set my first machine to foward all the traffic directed to
that domain?
Thanks for any help u can give me.
Sdav