Fedora Bind Setup help needed

[tech160s]

Hi All,
I am trying to setup a server on my local network that can run an
internet site available to internal local users by using the fully
qualified domain name. I run Fedora Core 4. I have setup dhcp and the
Fedora provided caching nameserver,  the internal clients can all
sucessfully lookup the outside world and obtain IP info from dhcp.
I have added some more zone files and listed them in /etc/named.conf
Restarting named and the zone files appear in /var/log/messages as
loaded ok. When I try to ping the web server from an internal client
using the FQDN, it sends the request out to the internet ISP DNS server
and of course this then fails.

please help

Regards, Richard.