In this paper, subspace-based algorithms for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein and Wiener models are presented. The proposed algorithms consist basically of two steps. The first one is a standard (linear) subspace algorithm applied to an equivalent linear system whose inputs (respectively outputs) are filtered (by the nonlinear functions describing the static nonlinearities) versions of the original inputs (respectively outputs). The second step consists in a 2-norm minimization problem which is solved via a Singular Value Decomposition.