Abstract. We proposed recently a new method for separating linearquadratic mixtures of independent real sources, based on parametric identification of a recurrent separating structure using an ad hoc algorithm. In this paper, we develop a maximum likelihood approach providing an asymptotically efficient estimation of the model parameters. A major advantage of this method is that the explicit form of the inverse of the mixing model is not required to be known. Thus, the method can be easily generalized to more complicated polynomial mixtures.