In the rich repertoire of design methodologies for uncertain nonlinear systems, the problem of unmodeled dynamics has thus far received little attention, We initiate the investigation of nonlinear systems with input unmodeled dynamics, First we show that even in their simplest forms, they can result in dramatic shrinking of the region of attraction and in finite escape time, In this paper we introduce a dynamic nonlinear damping design which guarantees global boundedness in the presence of input unmodeled dynamics, With this design we achieve global asymptotic stability for strict-feedback systems and output-feedback systems.