Cannot relay SMTP from outside subnet

Our Exchange server is doing something weird:

The exchange server is behind a firewall, IP=192.168.1.1.

When a user ON the subnet sends an email thru smtp, there is no problem, the message is delivered no matter what the recipient.

When a user is external to the firewall, only messages to the Exchange server’s domain get delivered. Any other emails (@yahoo.com, @whitehouse.gov, etc.) return errors that they cannot be relayed.

It is not a matter of Windows authenication, because there are subnet Macs with no authentication that have no problem sending mail.

This is not a firewall issue, because the messages get into the server, but it only won’t pass on certain ones.

As far as I can tell, I have very low security on the smtp server.

Any ideas?