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A new model of the human operator, termed the surge model, is developed. It is dual mode, containing a linearized constant coefficient model and an optimum second-order controller model. The equations describing its performance are written in the time domain. When the absolute values of the system error and of the first error derivative are less than certain specified bounds, the linear constant coefficient model is employed; and when the absolute values of the system error and of the first error derivative exceed these bounds, the optimum second-order controller model is employed. The surge model accurately predicts actual human operator performance in situations where the present widely used constant coefficient models yield unrealistic results, namely, when the signal being tracked contains discontinuous as well as continuous components, of either a random or a predictable nature. An Applied Dynamics 256 analog computer and a Control Data 3600 digital computer were employed, respectively, to simulate a real-time tracking problem and to solve the surge model equations characterizing the tracking task. Results presented in graphical form clearly indicate the superiority of the surge model in simulating tracking situations where discontinuities may occur.