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A method of system simplification having application to power-system dynamic-stability problems is discussed in the paper. The method is based on the geometric properties of Lyapunov functions, and is suitable for modelling higher-order systems that are expressed in state-variable form. Techniques are given for modelling both the free and forced responses. Two examples illustrating the application of this method are given. In the first example, simplification of a 4th-order system by this method is considered and the response of the resulting model is compared with the response of the model obtained by the eigenvalue-grouping method. In the second example, lower-order dynamic equivalents for an 11th-order differential equation describing the performance of a synchronous machine are derived. Advantages of this method over existing methods are discussed.