A new adaptive output feedback design using dynamic bounding is presented for actuator failure compensation of a class of nonlinear systems with unknown nonlinearities bounded by output-dependent functions and dynamic signals. The new features are that desired objectives can be achieved via a Lyapunov based design without using high gain type controllers and that it handles a larger class of systems. An adaptive scheme dealing with unknown actuator failures as well as system uncertainties is developed to achieve desired output tracking and closed-loop stability in spite of actuator failures.