In recent years there has been a considerable development in time seriesanalysis, represented mainly by alternative linear models able to describe more adequately the short and long term dynamics and by the renewed interest in modelling nonlinearities and asymmetries in economic and financial variables. Given the relevance of such variables in devising economic and monetary policy, it is of theoretical, as well as practical, importance to propose statistical methods appropriate to represent their dynamic behaviour. The aim of this work is to compare the forecasting performance of different models for the returns of some of the most traded exchange rates, namely the French Franc (FF/$), the German Mark (DM/$) and the Japanese Yen (Y/$). We compare the relative performance of some nonlinear models and contrast them with their simpler linear counterparts. Although we find evidence of noticeable forecasting gains from nonlinear models, the results are sensitive to the metric adopted to measure the forecasting accuracy.e.