After the war, the Allies occupied Germany, outlawed the Nazi Party and worked to purge its influence from every aspect of German life. The party’s swastika flag quickly became a symbol of evil in modern postwar culture. Although Hitler killed himself before he could be brought to justice, a number of Nazi officials were convicted of war crimes in the Nuremberg trials, which took place in Nuremberg, Germany, from 1945 to 1949. Source: http://www.history.com/topics/world-war-ii/nazi-party

Law No.2 issued by the Allied Control Council on October 10th 1945 banned the NSDAP and a whole host of other organizations.