The Axis counties were principally Nazi Germany, Fasist Italy (Until 1943) and Imperial Japan. Finland was an ally of Nazi Germany until 1944, but not strictly speaking a member of the Axis. Austria, Romania, Bulgaria and Hungary were also Nazi Allies during the war, although they ceased to be so when they either changed sides as Hungary did, or were invaded by Allied forces in the later stages of the war.
Although Spain was Facist under Franco it did not participate in the War as Franco felt to do so would incur Allied Invasion, although Spanish volunteers did serve within the Whermacht. Turkey was a neutral country during the war period, even though it had sided with the Germans and Austro-Hungarians in the Great War. Again this was to prevent possible invasion. It is interesting to note that during the war both the Allied and Axis Powers supplied Turkey with arms, notably aircraft, to try to draw her into the war.