We study the time-varying efficiency of nineteen members of the Federation of Euro-Asian Stock Exchanges (FEAS - an international organization comprising the main stock exchanges in Eastern Europe, the Middle East and Central Asia) by generalized Hurst exponent analysis of daily data with a rolling window technique. The study covers the six years of time period between January 2007 and December 2012. The results reveal that all FEAS members exhibit different degrees of long range dependence varying over time. We present an efficiency ranking of these members that provides guidance for investors and portfolio managers. Results show that the least inefficient market is Turkey followed by Romania while the most inefficient markets are Iran, Mongolia, Serbia and Macedonia. Throughout the considered time period, Turkey's stable Hurst exponent around 0.5 differs from others and shows characteristics of a developed financial market. For the federation members, strong positive relationship between efficiency and market liquidity is revealed. In the light of this fact, alternatives are suggested to improve market efficiency.