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This paper integrates the natural gas and hydrothermal systems in terms of power and gas optimal short- term operations planning and unit commitment. In this paper, the natural gas network model including storages and pipelines are integrated with hydrothermal systems to optimize short-term operation of both systems simultaneously. The proposed model considers the constraints at the hydrothermal system, natural gas extraction, natural gas storage operation and pipeline. The proposed model results in a large-scale mixed-integer nonlinear programming problem where the objective function is to minimize the integrated gas-electricity system operation costs. To solve the integrated electricity-gas optimal short-term planning problem an approach based on Dual Decomposition, Lagrangian Relaxation and Dynamic Programming is employed. A didactic integrated hydrothermal and gas system case study is presented. The proposed model shows the importance of the integration of the two systems in terms of operation, planning, security and reliability.