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This paper describes a new computational approach to the problem of the most economical operation of hydraulic plants in electric power systems, employing L. S. Pontryagin's maximum principle. The economical operation of a simplified model system is treated and the long range operation of a multireservoir system is considered. The relaxation method is successfully applied to the solution of optimal water usage policy in a model system of two reservoir-type and three regulating pondage-type hydraulic plants, with one equivalent thermal plant. Comparison is made between the maximum principle approach and dynamic programming. It becomes evident that the maximum principle is a powerful tool not only for the treatment of engineering problems, such as time-minimal control of servomechanisms, but also as a new technique of mathematical programming for the treatment of problems in mathematical economics.