We fly from Dusseldorf via Atlanta to Buffalo, both flights with Delta Airlines. Do we have to pick up the luggage in Atlanta and through the whole immigration procedure ??? We were told that the luggage is "checked through" (because Delta). What is right

Partly correct. If you pass through Customs, you will get back your baggage to process with your border documents. Your bags will be returned to Delta upon departure from customs and picked up in Buffalo. [Partially correct. When going though customs, you get your bags back to your documents. Your bags are sent to Buffalo.]

Jason Kilpatrick is correct in his response to Berndsollon's question. That's just the way it is. In fact I couldn't have said it better myself. Yeah, what he said! Enjoy your visit to the USA. I am glad that we could help you. Are there any other questions?