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In this paper, a sequential learning neural network, named as minimal resource allocating network (MRAN), is used to forecast monthly exchange rates between the U.S. dollar and the Deutsche mark, the British pound and the Canadian dollar. Five dominant economic structural exchange rate models are employed as the inputs of MRAN. Although the neural network cannot beat the simple random walk model without drift in out-of-sample forecast accuracy, it is better than the multilayer perceptron (MLP) neural network and the random walk model with drift in trend forecasting. The phenomena that the preferable structure of exchange rate model varies in different short periods are discovered from the simulation results. A simple model-competition methodology, purposing to choose the dominant model for next forecasting from the candidate models according to their previous short-term performance, is tested and found to improve the forecasting performance in forecast accuracy and direction accuracy.