Yes and no.

Following the defeat, most Nazi Party members who weren't imprisoned or executed went about living their lives. Some, however, were still holdouts. In West Germany there was the organization of the Socialist Reich Party (formed by a Wehrmacht veteran), until in 1956 it became the first party to be banned for being Nazi. Various other groups popped up here and there between 1945 and 1991, most of them being underground terrorist cells since Nazism was banned by the constitution.

In East Germany it was slightly different. The Socialist Unity Party attempted to reorganize the remaining Nazis into a positive political force called the Democratic Party of Germany. Ironically, this was meant to stop them from being active Nazis, but this effort failed miserably, because as soon as East Germany held open elections, the party started towing an explicit rightist line, and when reunification happened it turned straight up Neo-Nazi.

EDIT: The East German party was called the National Democratic Party of Germany, as is the current Neo-Nazi party in modern Germany.

EDIT 2: OK so the East German party was the National-Democratic Party of Germany, and the modern Neo-Nazi party, the National Democratic Party of Germany (no hyphen) is of West German origin. The N-DP dissolved after the wall came down.