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This paper examines the weak form of market efficiency of five major stock markets; four African equity markets and one developed market. The weekly market index returns of the EGX 30, NSE 20, NSE All Share Index, FTSE-JSE All Share Index and the S&P 500 Index were analysed for the period 1998-2008. To determine if the stylized fact of stock returns in African markets violate the random walk hypothesis, numerous econometric and statistical techniques are employed. These methods include the autocorrelation test, the unit test, linear and non-linear models. The results indicate that the African markets do not behave in a manner consistent with the weak form of market efficiency. These results provide a contrast between the emerging African markets and the developed markets. It suggests that African emerging markets have higher average returns and volatility than developed markets. We argue that if the market could be made less volatile, it has the potential to attract more investment because of its attractive returns. [ABSTRACT FROM AUTHOR]