This paper investigates the persistent excitation conditions under which the parameters in the fuzzy system model converge to their true values when the standard Mamdani type fuzzy system is constructed and the orthogonal projection parameter-tuning algorithm is used for nonlinear system identification. Algorithms are proposed accordingly for generating the input signals with persistent excitation property for the identifications of nonlinear moving average (N-MA) and second-order nonlinear auto-regressive moving average (N-ARMA) systems.