This paper attempts to study GARCH models with their modifications, in capturing the volatility of the exchange rates. The parameters of these models are estimated using the maximum likelihood method. The performance of the within-sample estimation is diagnosed using several goodness-of-fit statistics and the accuracy of the out-of-sample and one-step-ahead forecasts is evaluated using mean square error. The results indicate that the volatility of the RM/Sterling exchange rate is persistent. The within sample estimation results support the usefulness of the GARCH models and reject the constant variance model, at least within-sample. The Q-statistic and LM tests suggest that long memory GARCH models should be used instead of the short-term memory and high order ARCH model. The stationary GARCH-M outperforms other GARCH models in out-of-sample and one-step-ahead forecasting. When using random walk model as the naive benchmark, all GARCH models outperform this model in forecasting the volatility of the RM/Sterling exchange rates.