The Federation of Rhodesia and Nyasaland (aka Central African Federation (but not to be confused with the Central African Republic)) was a semi-independent state from 1953 to 1963. It consisted of the former self-governing colony of Southern Rhodesia, along with Northern Rhodesia and Nyasaland, both British Protectorates.
Formed at a time when Britain was under pressure to end colonialism, Rhodesia & Nyasaland was meant to be a sort of middle ground between the newly independent Black socialist states and the white-dominated states such as South Africa. However, the federation fell apart when the white minority failed to concede enough power.
Rhodesia and Nyasaland on Wikipedia