Accurate and sufficient detailed excitation system models are essential to the precise calculations of power system stability limits. This paper presents in detail a procedure for identifying excitation system models based on the on-line digital measurements from a plant transient recorder system. A solution algorithm for identifying parameters of the excitation system models is devised and implemented. The gradient averaging stochastic approximation method is employed to handle nonlinearity of the system models. Detailed numerical results based on the on-line measured data of Taipower system are included.