Abstract. In this paper, we propose and study a new on-line algorithm for learning a SVM based on Radial Basis Function Kernel: Local Incremental Learning of SVM or LISVM. Our method exploits the “locality” of RBF kernels to update current machine by only considering a subset of support candidates in the neighbourhood of the input. The determination of this subset is conditioned by the computation of the variation of the error estimate. Implementation is based on the SMO one, introduced and developed by Platt [13]. We study the behaviour of the algorithm during learning when using different generalization error estimates. Experiments on three data sets (batch problems transformed into on-line ones) have been conducted and analyzed.