double login window at OS X

I just installed TV 15 on a new portable Mac.
This one appears as the 3rd licensed Computer in my profile, which is ok.

As I tryed to open TV 15 on my destop Mac, I got a (grey) login window, asking for email an password.

As soon, as I klick on the password field, a new (white) window opens and ask me for username and password.

Since I only use my email-address and not a username, I entered these together with my password - but the login failed.
If I dismiss this second window and enter my password at first one, the second one appears again... With no success while trying to log on.

On the other Mac, there is no second logon window - and the email/password combination is accepted...

Any ideas?
Thanks
Dirk