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Radial Basis Function networks with linear outputs are often used in regression problems because they can be substantially faster to train than Multi-layer Perceptrons. For classification problems, the use of linear outputs is less appropriate as the outputs are not guaranteed to represent probabilities. We show how RBFs with logistic and softmax outputs can be trained efficiently using the Fisher scoring algorithm. This approach can be used with any model which consists of a generalised linear output function applied to a model which is linear in its parameters. We compare this approach with standard non-linear optimisation algorithms on a number of datasets.