This paper proposes a novelty neural network model by using generalized kernel functions for the hidden layer of a feed forward network (Generalized Radial Basis Functions, GRBF), where the architecture, weights and node typology are learned through an evolutionary programming algorithm. This new kind of model is compared with the corresponding models with standard hidden nodes: Product Unit Neural Networks (PUNN), Multilayer Perceptrons (MLP) and the RBF neural networks. The methodology proposed is tested using six benchmark classification datasets from well-known machine learning problems. Generalized basis functions are found to present a better performance than the other standard basis functions for the task of classification.