After a day of sending bugreports and other mail to 2K-support, I finaly got somewere. First they told me my PC was to old, but after a little argument I got this awnser:
"Thank you for the reply and yes, you are correct.
I did not noticed you had a NVIDIA GeForce GT 540M card in your computer. For some reason, it appeared much lower in your DxDiag. Therefore you do meet the minimum specs.
That being said, would you be able to provide us a copy of your crash-dump file (CivilizationVI.exe.dmp), located in Program files (x86)/ Steam/ steamapps/ common/ Sid Meier's Civilization VI/ base/ binaries/ Win64 Steam.
For the moment we do have a workaround. To by-pass the issue, you'll have to discover which A.I is causing the crash. In order to know which A.I is causing the crash, you'll have to pay attention to which Civilization's turn it falls onto immediately before the crash happens. Once discovered, reload your save, and declare war on that Civilization and hit "Next Turn". This should prevent the game from crashing."
I still have problems, since I havent met the civ. yet on one game, but at least they are working on it. I have sent the dumpfile again, and will update the situation here.