Hi Noel! Thank you for your further answer! (You are right with the demand of sending configs to end guessing, of course!)
Because of your persitently drawing I was encouraged to look for other reasons than the obvious ones. And I found my mistake, after all. Thank you! I used to set smtpd_sasl_exeptions_networks to $mynetworks because internal clients shouldn't been bothered by introducion of optional SMTP Auth at the SMTP port (25) during first tests some month ago. I'd overlooked that it was still active - and prevents $mynetwork clients from authenticate with SMTP Auth even at all ports, of course. Regards, Hasso