I'm an American citizen visiting Denmark. As I understand it, I can stay in the Schengen for a period of 3 months. I arrived in Madrid on May 15th and came to Denmark on the 19th. Am I required to return to the States and come back if I wish to stay longer? In case I do need to return, do I have to go on the 15th or the 19th? I also have a Polish passport with me through which I can stay in the EU indefinitely. Is it possible to have my American passport "stamped out" somewhere and switch the Polish one, thereby allowing me to stay?