Sign-In Required * 2

Each time iTunes starts automatically with iPhone or iPad connected to the PC I get the same scenario, a pop-up:

"Sign-In Required
Click Continue and sign in to check for downloads.
Apple ID + Password
Continue/Cancel"

and then the second one:

"Sign-In Required
Click Continue and sign in to check for downloads.
Apple ID + Password
Continue/Cancel"

It doesn't matter, if I enter my password or click cancel twice.

Until I either enter the password (twice) or click cancel twice, the synchronisation is paused.

As soon as I enter the password (twice) or click cancel twice, I am free to use iTunes.