[Exim] root cannot send mail on 3.36

Hi to all of you ;-))

One small question: I have exim 3.36 installed on my e-mail-gateway (on
RedHat 7.3).
While trying to send an e-Mail via SMTP from another linux box (SuSE 7.3),
exim bounces the e-mail telling me unrouteable mail domain web.de or any
other domain I try.
The problem only exists when sending as root from the linux box directly
via SMTP to our exim gateway.
When I send with another e-mail-adress like noone@??? everything is ok.

Maybe you have any ideas.
Please tell me if you need some more information! Thanx a lot,

Michael