Multihomed BIND will not respond to 2nd address

[Richard Blackwell]

I'm having to switch my entire network from the IP address space of one of
our ISPs to another.

I'm running BIND 8.2.5 on a RedHat 7.1 box with two NICs, each NIC with a
single IP address, one in each address space.  The OS install is fresh,
installed from CD yesterday, and I downloaded BIND from isc.org and compiled
it on the machine in question.

I have used the "listen-on" configuration directive in named.conf to tell
BIND to listen on both addresses.

My problem is:  I cannot get BIND to respond to any requests from any other
machine on the IP address in the new address space, but it responds
beautifully on the old IP.  If I run nslookup against BIND from the BIND
host itself, I can get replies back from either IP address.  As a test, I
have reconfigured BIND to not listen on each IP address, and got the
appropriate non-reponse I'd hoped I'd see.

The both IP addresses and the IP stack are working and correctly configured.
I can ping, ssh, telnet, and ftp the machine in question from another
machine on the network.

The only thing I can figure is that I've missed something in my BIND
configuration.  Any ideas?