This paper presents the optimal participation of strategic electricity and gas producers (SEPs and SGPs) in the coupled electricity and gas market of the day-ahead (DA) reserve regulation and energy type in accordance with the Energy Management Strategy (EMS). The deterministic model of this scheme has two bi-level problems, which refer to modelling of the participation of SEPs/SGPs in the DA energy and reserve markets. In any bi-level problem, the upper-level formulation minimizes the difference between the cost and revenue of SEPs or SGPs in these markets subjected to the operational model of these producers. In the lower-level formulation, the market clearing price (MCP) model is expressed in the problem such that the minimization of the energy cost of non-SEPs / non-SGPs are subjected to the electrical / gas network, electricity / gas generation units, and the reserve requirements model. In this scheme, load, renewable generation power, and reserve demand are uncertain. Hence, this paper proposes the robust modelling to achieve an optimal point in the worst-case scenario. Furthermore, the master-slave decomposition (MSD) method is suggested to reach the optimal solution at a low calculation time. Finally, the proposed scheme is simulated on the standard test system. The numerical results confirm its capability to achieve benefits for SEPs / SGPs along with the extraction of economic operation for energy networks.