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The research contribution of this thesis is the first known integrated architecture and feature selection algorithm for Radial Basis Neural Networks (RBNN's). The objective is to apply the network iteratively to determine the final architecture and feature set used to evaluate a problem. Additionally, this thesis compares three different classification techniques, Discriminant Analysis (DA), Feed-Forward Neural Networks (FFN) and RBNN's against several hard to solve problems. These problems were used to evaluate general classifier performance as well as the performance of the feature selection techniques. This thesis describes the classification techniques as well as the measures used to evaluate them. It next develops a new clustering technique used to determine the network architecture and the saliency measure used to select features for RBNN's. Next, the thesis applies these techniques to three general problems, Block-C, the University of Wisconsin Breast Cancer Data (UWBCD) and a noise corrupted version of Fisher's Iris problem. Finally, the conclusions and recommendations for future research are provided.