This paper presents a method for multi-period optimization of natural gas and electric power systems incorporating gas-fired power plants to analyze the impact of the interdependence between those commodities, in terms of cost and energy supply. The proposed method considers electricity network constraints, such as voltage profile, electrical losses, and limits of the transmission lines, as well as the technical restrictions on the gas network, such as the diameter, length, pressure, and limits for those variables. The proposed method was applied to a 12-bus electric network and a 7-node gas network, and several interdependencies between the electricity and the natural gas system network can be observed. The results show how the restrictions cause the behavior of the gas-fired power plants—in a low demand stage, it is restricted even when the gas-fired power generation prices are below the hydraulic generation prices, while in scenarios of higher demand, saturated cargo flows are observed, causing bus bar prices to be affected with higher operating costs. In this sense, the results of the variation in bus bar prices show little price stability in some bus bars in different stages, due to the behavior of the generation supply that is forced to operate by system restrictions.