This paper presents a new adaptive procedure for the linear and non-linear separation of signals with non-uniform, symmetrical probability distributions, based on both simulated annealing and competitive learning methods by means of a neural network, considering the properties of the vectorial spaces of sources and mixtures, and using a multiple linearization in the mixture space. The main characteristics of the method are its simplicity and the rapid convergence experimentally validated by the separation of many kinds of signals, such as speech or biomedical data. c 2002 Elsevier Science B.V. All rights reserved.