JEL classification: C5 G1Keywords: GARCH-M (1,1) Kalman filter Evolving Efficiency Test Arab stock markets Our goal is to examine whether Arab stock markets are becoming more efficient during the last decade thanks to organizational improvements and agents' learning. To achieve this goal a test of evolving weakform efficiency using GARCH-M (1,1) approach along with state-space time-varying parameters is implemented for 11 Arab stock markets for periods ending in March 2009, rather than studying their efficiency/inefficiency at a given point of time as commonly done. All markets show high sensitivity to the past shocks and are found to be weak-form inefficient. Moreover, the efficiency does not clearly improve towards the first quarter of 2009 and negatively reacts to contemporaneous crises, except temporary subperiods of efficiency improvement for the largest markets. This contrasts with mature markets and reveals the ineffectiveness of the reforms so far undertaken and calls to intensify efforts to expand and deepen these markets besides improving their liquidity and transparency and counteracting the shortcomings of the large individual trading by enhancing investment culture and spreading institutional trading.