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In this paper we present a new approach to solving the power system dynamic simulation problem using the Generalised Minimal Residual (GMRES) algorithm. This is one of the several methods in the family of Conjugate Gradient methods for solving systems of equations of the form Ax = b. Although some of these methods require A be symmetric positive definite, GMRES has no such restriction. The technique is illustrated on a 39 bus, 10 machine power system using the Cray Y-MP.