Abstract: The classification mechanisms of feedforward two layered radial basis function(RBF) and linear basis function(LBF) networks as well as the methods of optimally determining their structures and initial parameters were studied. The viewpoints were presented that the centers and widths of Gaussian kernels in RBF networks should be determined by a self learning procedure, that a few new kernels be naturally come into being according to which class some labeled patterns are misclassified to, and going a step further, that some current kernels be automatically deleted if their effects on the test data are too trivial to be worthy of mention. The reason why the classification threshold of a feedforward two layered LBF network with sigmoid activation function should be 0.5 was clarified in theory. And finally, a kind of improved RBF(IRBF) networks consisting of a two layered RBF and a two layered LBF one were proposed.