Hello, I am flying to Hungary (from Chicago) in January. The flight on the way back to the U.S. in July will have me stopping in Dusseldorf but only for 35 minutes. Since this is the last leg before flying back to the U.S., will immigration be time consuming to get through? Is 35 minutes possibly enough time? Has anyone encountered this as a problem before? Any info would be great!

Hungary and Germany both belong to what is called the Schengen Area. Travel between them is passport free. No immigration or customs when you change planes at Dusseldorf.

great! thank you so much!

"No immigration or customs when you change planes at Dusseldorf."

Hmm...

Whenever I've flown from Germany to a non-Schengen destination lately I've had to go through outbound emigration control.

No mega deal, but there's often someone who's messed their paperwork in front of you. May well only take 5 mins - but if you're running tight, it can feel like an hour.

As flanner says.
There will be passport control for leaving the Schengen area in Düsseldorf.
In addition, there will be another security checkpoint with x-ray and a hand search of cabin luggage near the departure gates as for any flights bound for North America.
I doubt that 35min is within minimum connecting time at DUS for changing from a domestic/Schengen to an intl/US flight.
Unless you have mixed up the departure time in DUS with the boarding time for the connecting flight, I would address the airline and ask what they think of it.