[1] In 1946, he became a member of the Liberal Democratic Party of Germany (LDPD), and was until 1951 an official of the LDPD local district association (Kreisverbandes) in Dresden and the state association (Landesverbandes) of Saxony.

After the events of the 17 June 1953, he was suspected as a foreign agent and temporarily detained by the Stasi.

Between 1954 and 1959, he completed a correspondence PhD in Law from the Walter Ulbricht Academy of Law and Political Science in collaboration with Manfred Gerlach; his thesis was entitled "Function and development of the Liberal Democratic Party of Germany in the multi-party system of the German Democratic Republic".

In 1967, he succeeded Hilde Benjamin as Minister of Justice, a position he held until 1972.

After the fall of the Berlin Wall, Wünsche was again made Minister of Justice in the governments of Hans Modrow and Lothar de Maizière.