The global asymptotic stabilization problem for a general class of uncertain nonlinear systems with dynamic input uncertainties (input unmodeled dynamics) is considered. The system structure addressed in this paper is comprised of a nominal system (which can have a general nonlinear dynamics structure and is assumed to have a nominal control law to stabilize the nominal system) and an appended input unmodeled dynamics. The proposed approach is based on a control redesign utilizing the nominal control law and incorporating a singular-perturbation-like dynamic system extension along with a dynamic scaling to address the dynamic input uncertainties. The control input uncertainty structure is modeled through an uncertain non-affine function of the control input and the unmeasured state of an uncertain input unmodeled dynamics subsystem. The proposed control redesign approach is applicable to a wide class of nonlinear systems including triangular as well as non-triangular system structures as long as a set of structural and inequality conditions on the system dynamics are satisfied and provides a global robust output-feedback stabilizing controller.