Exchange rates forecasters usually assume that local methods (nearest neighbour) dominate the global ones (neural networks or genetic programming, for example). In this article, first, we use different generalizations of the standard nearest neighbours to predict the dynamic evolution of the Yen/US$ and Pound Sterling/US$ exchange rates one-period ahead. Second, we compare our results with those employing global methods such as neural networks, genetic programming, data fusion and evolutionary neural networks. Finally, we find out the existence of predictable structures periods ahead. Our results reveal a slightly but significant forecasting ability for one-period ahead which is lost when more periods ahead are considered, and no important predictive differences between local and global methods have been found.