This paper considers the generalized autoregressive conditional heteroscedastic approach in modelling exchange rate volatility in a panel of nineteen of the Arab countries using daily observations over the period of 1^st January 2000 to 19^th November 2011. The paper applies both symmetric and asymmetric models that capture most common stylized facts about exchange rate returns such as volatility clustering and leverage effect. Based on the GARCH(1,1) model, the results show that for ten out of nineteen currencies the sum of the estimated persistent coefficients exceed one, implying that volatility is an explosive process, in contrast, it is quite persistent for seven currencies, a result which is required to have a mean reverting variance process. Furthermore, the asymmetrical EGARCH (1,1) results provide evidence of leverage effect for majority of currencies, indicating that negative shocks imply a higher next period volatility than positive shocks. Finally, the paper concludes that the exchange rates volatility can be adequately modelled by the class of GARCH models.