The aim of this paper is to compare the forecasting performance of SETAR and GARCH models against a linear benchmark using historical data for two bilateral dollar exchange rates, namely the Japanese Yen and the British Pound. The analysis is carried out with series sampled at weekly and daily frequencies. The relative performance of the models is evaluated on point forecasts and on interval forecasts. Point forecasts evaluation tends to favour on average the linear models, though the analysis produces some evidence of forecasting gains from nonlinear models in sub-samples characterised by stronger non-linearities. When we evaluate the validity of interval forecasts, the results clearly favour the GARCH model and show that the AR and SETAR forecasts are not correctly conditionally calibrated.