This paper examines the spillovers in time and frequency from emerging (Brazil, Russia, India, China), developed (US, UK, France, Germany and Japan) stock markets and oil prices toward seven African stock markets. The spillovers are examined from 2005 to 2016, taking into account the recent financial crises and the recent oil prices fall. We combine the generalized Vector AutoRegressive (VAR) framework and the Maximum Overlap Discrete Wavelet Transform (MODWT) to obtain the spillovers at different time scales. The results show that the relationships between African stock markets, world stock markets and oil prices depend on time scales. African stock markets could be a way of capital diversification for global stock markets at scale 1 (2-4 weeks) and for investors active in the oil market at scale 2 (4-8 weeks).