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there is gui but no login on console after boot


Recently I have noticed that there is no login prompt on my consoles.
X11 starts and I can use my system (I can also start a gui console).

I have upgraded my system to Debian 9 and hoped to get this issue solved seamlessly. However, there is still no prompt.

Could you suggest how to debug such an issue?

I googled and found only one possibility: something stays in the foreground at startup. But I do not find anything.

Thanks for your suggestions,