Abstract: The space heating system with fuel cells (11) has a connection to a public electrical network (50). In this system a fuel (B) can be supplied to the fuel cells in gaseous form through a main gas valve (200) for the production of thermal and electrical energy. The main gas valve has a control which, on an interruption of the current supplied, results in an automatic operating shutdown. The possibilities exist for the system to feed the electrical energy at least partly into the network and to deliver the thermal energy to a heating circuit which is operable with electrical energy from the network. An electrical inverter (4), with which direct current of the fuel cells can be converted into alternating current, can be operated in two operating states, on the one hand, for a feed into the public network, and, on the other hand, for a feed into the island network of the system.