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A new Lyapunov function for multimachine power systems with and without speed governors is generated using the variable gradient method. The method is based upon the assumption of a variable gradient function from which both V(x) and V¿¿(x) may be determined. The n unknown elements of each of the n components of the variable gradient are determined from constraints on VV¿¿(x) and the generalised curl equations. The procedure given is suitable for any type of speed governor with any number of state variables. A 4-machine power system is tested and studied using both the classical step-by-step method and the Lyapunov second method. A comparative analysis between those methods indicates a great time saving for the second method. The effect of machine parameters on the critical clearing time is also investigated.