Due to depletion of fossil fuel resources and public concern on climatic change, integration of natural gas and electrical power systems for improving sustainability and efficiency draws broad interests. However, operations of gas and power networks lie in different time-scales. Hence, it is necessary to consider such distinguished characteristics when investigating integration of these two systems. Under these circumstances, this paper derives dynamic energy flow equations in natural gas system. And multiple time-period optimal power flows in gas and power systems are coupled with bi-directional energy flow. Proper assumptions are made to linearize the formulated optimization problem while maintaining dynamic behavior of gas flow in pipes. Simulation results demonstrate effectiveness and accuracy of the proposed modeling techniques. The proposed method is suitable for large-scale integrated gas-electric systems.