We present two dual versions of a multi-input/multi-output (MIMO) Steiglitz-McBride identification method, and give an analytic description of the set of the possible stationary points. As in the scalar case (Regalia and Mboup 1992, Regalia 1995), the description is given in terms of first-and second-order interpolation constraints on the model impulse response and covariance sequences, respectively. The constraints are related to the theory of M-Markov covariance equivalent realizations and generalize the works of Inouye (1983) and King et al. (1988). It is shown that the description is intimately connected to a class of first- and second-order matrix-valued interpolation problems of tangential Nevanlinna-Pick type. Such problems are studied by Alpay et al. (1996). We also examine the quality of the model furnished in reduced order cases, and show in particular that the mismodelling error at any stationary point of the method can be bounded in terms of the Hankel singular values of the unknown system. The bound so obtained compares favourably with known bounds from L-2- and Hankel-norm model reduction.