The purpose of this research is to investigate the forecasting performance of Artificial Neural Network models applied to foreign exchange rates. The study concentrates on the behavior of forecasts of exchange rates generated from the radial basis function (RBF) network models where little previous work exists;Exchange rates examined are the German mark/US dollar, Japanese yen/US dollar, and Italian lira/US dollar. One-step-ahead forecasts from univariate and multivariate RBF models are compared with those generated from ARIMA models, random walk forecasts and the forward rates. Interest rates and the money supply (M1) are used as explanatory variables in the multivariate analyses;Out-of-sample evaluation criteria include root mean squared error, "correct direction", and "speculative direction". Hypothesis tests are used to assess if differences in forecast accuracy from different models are significant and to assess if models can predict the direction of change with statistical significance. The tests employed are the Modified Diebold Marino test [Harvey et al. (1997)], the Pesaran-Timmerman (1992, 1994) non-parametric market timing test, and the chi2 test of independence [see Swanson and White (1997)];The main results of the study indicate that RBF models may be a useful alternative to the other models considered for forecasting exchange rates. In particular, out-of-sample forecasting results indicate that some multivariate RBF models using interest rates as economic variables do have forecasting value for some exchange rates. In the presence of interest rates, the M1 variable does not seem to possess much explanatory power for forecasting the three exchange rates.