This contest comprises a selection of topics that focus on African stock market performance. The main factor in this analysis is to examine the dynamic behavior of stock returns in a number of emerging stock markets from Asia and Africa, the efficiency in pricing securities as well as the relation between exchange rate and dynamics of equity returns. The purpose of this study is to contribute to the debate by examining some issues concerning the efficiency of market and the relation between exchange rate and equity returns. These issues have not been examined so far for both Asian and African stock markets together, so this paper attempts to fill that gap by addressing the following objectives ,which are (1) to examine the Random Walk Hypothesis (RWH) for stock prices in Asian and African emerging Markets , (2) to determine whether exchange rates affect tests of equity returns in emerging markets, and (3)to investigate whether large capitalization stocks follow a random walk .The main significance of our study of these objectives is the use of the latest test methodologies in analyzing an investment area that is growing in the emerging stock markets.