Bit of a wide question...like any other country the individual states have their own Aviation Authority (CAA/DGAC) as required by ICAO who are responsible for airworthiness, safety, licensing etc. etc.
In some cases particularly the French speaking nations you may find some of the technical oversight functions are contracted out to the likes of Bureau Veritas but with overall co-ordination/control remaining with the authority.
Africa and its states are just like any other continent/state in terms of administration and operation...