An adaptive control scheme to achieve stability and output tracking is presented for the output-feedback nonlinear plant with unknown actuator failures. A state observer is designed for estimating the unavailable plant states, based on a chosen control strategy, in the presence of actuator failures with unknown failure values, time instants and pattern. An adaptive controller is developed by employing the backstepping technique, for which parameter update laws are derived to ensure asymptotic output tracking and signal boundedness of the closed-loop system, as shown by detailed stability analysis.