This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models, in which the regressor space is partitioned into polyhedra with affine submodels for each polyhedron. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where the estimation data only seldom switches between the different submodels, we also suggest a way of trading off between optimality and complexity by using a change detection approach. (C) 2003 Elsevier Ltd. All rights reserved.