Undesired complex hysteretic nonlinearities and complex log(t)-type creep dynamics with asymmetrical branching characteristics are present to varying degrees in virtually all smart-material based sensors and actuators provided that they are driven with sufficiently high amplitudes. In motion and active vibration control applications, for example, these nonlinearities can excite unwanted dynamics which leads in the best case to reduced closed-loop system performance and in the worst case to unstable closed-loop system operation. From the practical point of view It is extremely useful to cancel these types of nonlinearities by a feedforward compensation strategy. Therefore, the present article describes a new compensator for these types of actuator nonlinearities with large creep processes based on the so-called Preisach approach. It discusses a rigorous existence, uniqueness and stability proof for the compensator. Moreover, it deduces an algorithm for the calculation of the compensator in real-time applications and presents some experimental results which document the applicability of the method for practical applications.