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IN THE PAST FEW YEARS a great deal of interest has developed in the analysis of nonlinear systems. Much of this has been the result of the great strides taken in the field of control systems. However, nonlinearities have a way of appearing in many forms in many different types of systems. In fact, almost all systems when analyzed carefully have some degree of nonlinearity, and the linear representations are only approximations. In this paper some of the techniques that originated in control system work are extended to the analysis of a power system's stability, and in the process some new methods of analyzing nonlinear systems are presented.