Multiple variance ratio tests, in rolling window procedure, were applied to weekly data (expressed in local and US dollar currencies) for five stock markets in the Middle East and North Africa during 1995-2011. Results indicated that the big and liquid stock markets of Israel and Turkey are ranked as the most efficient. The Egyptian and Moroccan stock markets converged towards efficiency by 2002, due to remarkable improvements in liquidity and information dissemination, whereas the Jordanian stock markets restored its efficiency at the end of the study period. Exchange rates did not matter in determining the dynamics of share returns for equity markets examined.