The ideas of adaptive nonlinear damping and changing supply functions were used to counteract the effects of parameter and nonlinear uncertainties, unmodeled dynamics and unknown bounded disturbances. The high-gain observer was used to estimate the state of the system. A robust adaptive output feedback control scheme was proposed for nonlinearly parameterized systems represented by input output models. The scheme does not need to estimate the unknown parameters nor to add a dynamical signal to dominate the effects of unmodeled dynamics. It was proved that the proposed control scheme guarantees that all the variables in the closed-loop system are bounded and the mean-square tracking error can be made arbitrarily small by choosing some design parameters appropriately. Simulation results demonstrated the effectiveness of the proposed robust adaptive control scheme.