[Exim] Exim PPP localhost mailing problem

I am running  Exim version 3.03 #1 built 04-Aug-1999. My
problems stem from local mail delivery. Whenever I try to send mail to
user@localhost, exim seems to strip the localhost and replace it with the
remotehost-- making it user@???.
    Because I am using PPP my domain name does not have an '.com,
.net etc', so it is just 'hostname'. The weird thing is that if there is a
system error, ie. someone trying sudo when they don't have permissions to
do so, exim is used to send mail to localhost and successfully does that.
The problem happens when any user, including root, tries to send mail to
another user on the local host.