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Multiple-input multiple-output systems are increasingly important in a great number of fields, as is the case with telecommunications, robotics, biology, neuroscience, etc. In this paper, Volterra models are applied to a class of MIMO nonlinear systems, showing that linearity with respect to the coefficients ensures the availability of a global solution for the identification problem. The applicability of traditional learning algorithms, as Least-Mean-Square (LMS), is conditioned by eigenvalue spread, mainly dominated by nonlinear effects. This convergence issue and others are shown by means of a theoretical treatment and some examples.