A global nonsmooth stabilization scheme is presented for a class of nonlinear cascaded systems with uncontrollable linearization. A stepwise constructive control methodology is proposed for the driving subsystem by using the adding a power integrator technique. Under suitable conditions and based on homogeneous properties, it is proved that the stabilization of the driving subsystem implies the stabilization of the overall cascaded system. Due to the versatility of the adding a power integrator technique and homogeneous properties, the proposed controller not only can be used to stabilize the cascaded system asymptotically, but also is able to lead to an interesting result of finite-time stabilization under appropriate conditions. (C) 2012 Elsevier Ltd. All rights reserved.