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Davison's method is used to reduce the order of a one machine infinite bus system with excitation control from a tenth to a fourth order System. This is accomplished by first reducing the machine from seventh to third order and the excitation system from third to first order and then combining these models to form the reduced order model of the one machine infinite bus system. It is shown that the eigenvalues which predict the natural and introduced rotor oscillations are accurately preserved by this method. Also, a method of combining reduced order models of machines to form dynamic equivalents of multimachine systems is set forth. Here, Davison's method is used to obtain a reduced order model of each machine whereupon approximations are used to achieve a simple means of combining these reduced order models to form a dynamic equivalent of a two machine system. This technique is shown to be sufficiently accurate for dynamic stability investigations. It appears that the method of reduction presented in this paper may offer advantages in the analysis of power system dynamics.