[exim] External mail problems

I have Exim4 running on a fully updated Debian server . I enabled the Internet setup option and checked the configuration files for ensuring that all of the necessary transports and routers were enabled . Exim4 refuses to send external messages . It can send local messages , but when I send to an outside address , it reports ( in the log ) a retry time-out failure of some sort . It is connected to the local network and to the Internet . I have changed to a single configuration file arrangement and have enabled and attempted to employ absolute I. P. addressing , but the messages still fail . Help me .

Frank Trampe