This paper aims to check whether the index (DWX) of Damascus Stock Exchange (DSE) is characterized by some of the stylized facts of most of the international and Arab stock markets, as: Volatility Clustering, Reversion to the Mean, and the Leverage Effect. The GARCH and EGARCH models were applied using the returns series of DWX for a period from 31/12/2009 till 16/4/2013. The findings showed that DSE is characterized by: Volatility Clustering, meaning that large volatility today will be followed by large volatility tomorrow, Leverage Effect, meaning that volatility tends to rise more after a negative shock that a positive one, But the DWX is not characterized by the reversion to the mean process, due the explosive volatility of the index.