Abstract: To solve the problem that the neural networks cannot directly approximate the nonlinear hysteresis which is characterized by multi-valued mapping, a new expanded input space is proposed in this paper. A dynamic hysteretic operator is constructed to represent the rate-dependent characteristic of the dynamic hysteresis. Then with the introduction of the input variable, input change-rate and dynamic hysteretic operator, a new expanded space is constructed. Hence, the multi-valued mapping of the dynamic hysteresis can be transformed into a one-to-one mapping on this expanded input space. Then, the neural networks are implemented for the identification of the dynamic hysteresis based on the proposed expanded input space. The proposed model is simple in structure and available for on-line updating to adapt to the environmental changes. Finally, the application of the proposed approach to the identification of a piezoelectric actuator is presented.