This paper presents a non-linear moving average model with exogenous inputs (NMAX) and a non-linear auto-regressive moving average model with exogenous inputs (NARMAX) respectively to model static and dynamic hysteresis inherent in piezoelectric actuators. The modeling approach is based on the expanded input space that transforms the multi-valued mapping of hysteresis into a one-to-one mapping. In the expanded input space, a simple hysteretic operator is proposed to be used as one of the coordinates to specify the moving feature of hysteresis. Both the modified Akaike's information criterion (MAIC) and the recursive least squares (RLS) algorithm are employed to estimate the appropriate orders and coefficients of the models. The advantage of the proposed approach is in the systematic design procedure which can on-line update the model parameters so as to accommodate to the change of operation environment compared with the classical Preisach model. Moreover, the obtained model is non-linear in variables but linear in parameters so that it can avoid the problem of sticking in local minima which the neural network based models usually have. The results of the experiments have shown that the proposed models can accurately describe static and dynamic behavior of hysteresis in piezoelectric actuators.