The rapidly increasing share of renewables in energy systems is reducing the primary fossil energy and CO2 emissions associated with the electricity consumption from the grid. In the coming years, there might also be a partial gas grid decarbonisation by means of biomethane, synthetic methane and hydrogen injections into the pipelines. Therefore, the competitiveness of polygeneration systems will have to be determined taking into account exogenous network parameters. This work investigates on how energy savings, emissions reduction and cost-effectiveness of combined heat and power (CHP) plants are affected by electrical RES (RESEL) and Substitute Natural Gases (SNGs) increase in energy networks. For RESEL share in the national grid higher than a threshold value ranging in 50% and 60%, natural gas CHPs do not provide energy and emission savings. Furthermore, the rapid reduction in RESEL costs could correlate their wide deployment with a decrease in electricity price, reducing the cost-effectiveness of gas-driven CHPs. Greening the gas grid enhances the threshold value and it can partially preserve those technologies. Nevertheless, the SNGs production cost is still very high. Therefore, if their injection increases the gas price for end-users, energy and environmental benefits will be offset by the loss of CHP cost-effectiveness.