In Hungary, Austria, Poland and Romanina you will need an invitation letter from the hunting service who you will be hunting with. You will declare the firearm at customs, airport or border, and present the invitation letter and receive a permit that is good for the length of stay in that country. You must check out with customs when you leave. Ensure you bring the firearm and ammo that is listed on the invitation letter. If flying Luftansa, make sure when you purchase tickets that you tell them then that you will be transporting a firearm, they like to know before hand. Driving across Countries you are not hunting in can be a problem.
