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The direct method of Liapunov is applied to the problem of power system stability. The method is first compared with the phase plane technique and equal-area criterion, with all three approaches giving identical results for the equivalent 1-machine system. A Liapunov function for the 3-machine system is developed, and conservative prediction of stability is possible if the machine velocities and angles are known at the time of final system disturbance. The method is easily extended to multimachine systems. Further work is needed in the area of easier determination of better Liapunov functions and the inclusion of such items as resistance, regulator action, governor action, and damping torques.