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This paper presents a new adaptive procedure for the linear and nonlinear separation of signals with nonuniform, 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. Moreover, the paper proposes the fusion of two important paradigms-genetic algorithms and the blind separation of sources in nonlinear mixtures. In nonlinear mixtures, optimization of the system parameters and, especially, the search for invertible functions is very difficult due to the existence of many local minima. The main characteristics of the methods are their simplicity and the rapid convergence experimentally validated by the separation of many kinds of signals, such as speech or biomedical data.