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This paper develops an adaptive output feedback control scheme for a class of nonlinear systems with state-dependent nonlinearities in the presence of unknown actuator failures. A robust backstepping feedback control law is derived to effectively handle the state estimation error due to such uncertain nonlinearities. An adaptive actuator failure compensation scheme is designed to ensure closed-loop signal boundedness and desired output tracking performance. An application to controlling the angle of attack of a nonlinear aircraft model in the presence of elevator segment failures is studied and simulation results are presented to illustrate the effectiveness of the adaptive actuator failure compensation design.