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This paper describes a new method for estimating critical clearing times for multimachine systems which dispenses with the calculation of post-fault swing curves. The theoretical basis of the method involves a study of trajectories in the post-fault state space near unstable equilibrium points. Results for a 15- machine system are described and a comparison is made with Lyapunov's direct method. Also described are some results concerning the modes of instability of a multi-machine system.