Abstract: The stabilization of nonholonomic dynamic systems with bounded inputs is studied. It is demonstrated that under appropriate assumptions Lagrange's equations, including classical nonholonomic constraints, can be transformed to the extended chained-form system. By using the sliding mode approach and a multi-step control strategy, a new controller is presented, which can not only satisfy the control constraints but also stabilize the system to an arbitrarily small ε-neighborhood about its equilibrium in a finite time. The proposed method is used to stabilize a mobile robot and the simulation result shows that the approach is effective.