The paper presents a constructive control design for integrator backstepping in nonsmooth systems. The approach is based on non smooth analysis and Lyapunov stability for nonsmooth systems and is similar in spirit with the robust control designs that have appeared in literature, but is applicable to a larger class of systems. The backstepping controller is first applied to the case of a unicycle driven by a new discontinuous kinematic controller yielding global asymptotic convergence with bounded inputs. Then it is used to implement a sliding mode controller in a hybrid system. Simulations results not only verify the convergence properties but also reveal the ability of the new backstepping controller to suppress chattering. (C) 2003 Elsevier Science Ltd. All rights reserved.