In recent years there has been a considerable development in modelling nonlinearities and asymmetries in economic and financial variables. The aim of the current paper is to compare the forecasting performance of different models for the returns of three of the most traded exchange rates in terms of the US dollar, namely the French franc, the German mark and the Japanese yen. The relative performance of nonlinear models of the SETAR, STAR and GARCH types is contrasted with their linear counterparts. The results show that if attention is restricted to mean square forecast errors, the performance of the models, when distinguishable, tends to favour the linear models. The forecast performance of the models is evaluated also conditional on the regime at the forecast origin and on density forecasts. This analysis produces more evidence of forecasting gains from nonlinear models.