In this paper, we propose a model predictive control (MPC) algorithm for switched nonlinear systems under average dwell-time switching signals. Assuming that a stabilizing MPC controller exists for each of the subsystems, we show that recursive feasibility of the repeatedly solved optimal control problem and asymptotic stability of the closed-loop switched system can be established if a certain average dwell-time condition is satisfied. If the switching times are unknown a priori and cannot be detected instantly, the MPC controller calculated for the previously active subsystem might not be stabilizing for the newly activated subsystem, thus possibly leading to an unstable closed-loop system. It is shown that if the switches can be detected fast enough, then still ultimate boundedness in an arbitrarily small region around the origin can be ensured, i.e., the proposed MPC algorithm is inherently practically robust with respect to small errors in the detection of the switching times. Finally, we apply our results to a continuous stirred-tank reactor (CSTR) with two different modes of operation. (C) 2012 Elsevier Ltd. All rights reserved.