The subject of this paper is identification of discrete time nonlinear dynamical systems when the system dynamics are defined by a discontinuous nonlinear function with the location of the discontinuity unknown. By representing the nonlinear function using both a parametric term to capture the continuous part and a non-parametric term to capture the discontinuous part, we present an identification algorithm along with conditions for recovery of the true nonlinearity. (C) 2013 Elsevier Ltd. All rights reserved.