Thank you for your response.
Unfortunately, the solution for my problem is not on this page.
Mail is working fine on my ipad and iphone but not on my imac since the last upgrade.
I can hear mail coming in, but I donot see it on my screen.
Now I tried to do the installation again with the lion settings i.s.o. ml
and .............. yes, it is working!
I am a very happy woman again.