In this paper, a novel learning strategy for radial basis function networks (RBFN) is proposed. By adjusting the parameters of the hidden layer, including the RBF centers and widths, the weights of the output layer are adapted by local optimization methods. A new local optimization algorithm based on a combination of the gradient and Newton methods is introduced. The efficiency of some local optimization methods to Update the weights of RBFN is Studied in solving systems of nonlinear integral equations. (C) 2009 Elsevier Ltd. All rights reserved.