This paper considers the stabilization problem for a class of switched nonlinear systems under arbitrary switching. Based on the backstepping method and the control Lyapunov function approach, it is shown that, under a simultaneous domination assumption, a switched nonlinear system in strict-feedback form can be globally uniformly asymptotically stabilized by a continuous state feedback controller. A universal formula for constructing stabilizing feedback laws is presented. One example is included for verifying the obtained results. (C) 2008 Elsevier Ltd. All rights reserved.