Egypt was technically neutral, but Cairo soon became a major military base for the British forces. This was because of a 1936 treaty which gave Britain the right to station troops on Egyptian soil in order to protect the Suez Canal.
Yugoslavia began the war as a neutral but Yugoslavia's Regent signed the Tripartite Treaty on March 25th, 1941, and met an anti-Nazi coup d'état when he returned on March 27th. This led to German occupation from April 6th1941.
France surrendered to Germany on June 22nd1940, and the Vichy government was installed, which cooperated with the Germans. However, substantial French forces escaped the German advance or switched sides and continued to fight on the Allied side as Free French.
French colonies initially fought alongside their parent country. When France surrendered most recognised the Vichy government.