This paper describes an adaptive system for controlling the tonal vibration of a single-degree-of-freedom system with nonlinear damping. The adaptive control system consists of a force actuator in parallel with the suspension, which includes the nonlinear damper, and a velocity sensor mounted on the mass. The adaptation of the controller is done once every period of the excitation. Because the response of the nonlinear system changes with excitation level, conventional adaptive algorithms, with a linear model of the plant, can be slow to converge and may not achieve the desired performance. An on-line observer is used to obtain a describing function model of the plant, which can vary with the excitation level. This allows the adaptive control algorithm to converge more quickly than using a fixed plant model, although care has to be taken to ensure that the dynamics of the observer do not interfere with the dynamics of the adaptive controller.