Abstract: It is presently customary in a high-temperature fuel-cell system to divide the cathode waste gas, in particular, into two subflows, of which one is recirculated again to the cathode and the other is removed for heat utilization. The bifurcation is carried out at relatively high technical costs at about the operating temperature of the fuel cell at the gas outlets themselves. In order to reduce that cost, the entire cathode waste gas is fed through a heat exchanger to a bifurcation having two branch pipes. The first branch pipe opens through an air addition point and the heat exchanger into the cathode and the second branch pipe opens into a temperature-increasing device. In this way, a bifurcation of the hot cathode waste gas is avoided and the heat of the entire cathode waste gas is used to heat the cathode waste gas subflow fed back into the cathode. The invention can preferably be used, in particular, for fuel cells having operating temperatures above 600.degree. C.