Active material actuators, sometimes referred to as "smart" actuators, are gaining widespread use for control actuation. Many of these actuators exhibit hysteresis to some degree between their input and output response. There exists an extensive body of research concerning the modeling of hysteresis for the linearization, or compensation, of these hysteresis nonlinearities. However, the models have typically been identified off-line and mainly used in open-loop compensation. When the identified models do not exactly match the actuator nonlinearities, the compensation can create an error between the desired and actual control output. The hysteresis for several of these actuators has been shown to evolve over time, and can render a fixed hysteresis model inadequate to linearize the hysteretic nonlinearities. This paper presents an adaptive hysteresis model for on-line identification and closed-loop compensation. Laboratory experiments with a shape memory alloy wire actuator provide evidence of the success of the adaptive identification and compensation. In addition, the means of determining the saturation of the SMA using updated information from the adaptive hysteresis model is provided.