[Exim] Routing mail to a host on internal network - no DNS

Hello,

I have an Exim server set up and running well to receive Internet
email and deliver it locally to user mailboxes in /var/spool/mail. The
system is Debian 2.1 with the standard Debian Exim package installed.
I've added entries to /etc/aliases and set up a default for any
inbound mail that doesn't match a specific name to go to the admin's
mailbox. All this work great.

I'd like to be able to redirect inbound mail for particular users to
another mail server on a host that is on the internal 192.168.x.y
network. The Exim mail server also acts as a firewall/NAT box.

When I add a line like the following to /etc/aliases:

thisuser: thisuser@???

the message is bounced by Exim saying "unrouteable mail domain". The
machine internalhost.mydomain.com cannot be looked up with DNS, but it
*is* the /etc/hosts table on the Exim machime.

Can someone please explain how I can get this to work?

Thanks very much.

Denny Fox