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This paper presents a new Maximum Likelihood (ML) based approach to the separation of convolutive mixtures of unobserved sources in the presence of Additive Gaussian Noise (AGN). The proposed method proceeds in two steps. First, the mixing system coefficients are estimated in the ML sense and, afterwards, this information is employed to attain source separation according to either the ML or the linear Minimum Mean Square Error (MMSE) criteria. System coefficient estimation is carried out in a block-iterative way using an extension of the Expectation Maximization (EM) method. Both deterministic and stochastic (Monte Carlo) implementations of the resulting estimation algorithm are considered. The proposed algorithms rely on the knowledge of the sources joint probability density function (p.d.f.). This is a fairly realistic assumption in applications such as digital communications but computer simulations reveal that it is not an stringent requirement. The proposed estimation algorithm can be successfully used with a tentative p.d.f. when this is not known a priori.