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Even though multilayer perceptrons and radial basis function networks belong to the class of artificial neural networks and they are used for similar tasks, they have very different structures and training mechanisms. So, some researchers showed better performance with radial basis function networks, while others showed some different results with multilayer perceptrons. This paper compares the classification accuracy of the two neural networks with respect to training data set size, and shows the performance of the two neural networks can be differently dependent on training data set size. Experiments show the tendency that multilayer perceptrons have better performance in relatively larger training data sets for some data sets, even though radial basis function networks have better performance in relatively smaller training set size for the same data sets. The experiment was done with four real world data sets.