A fuel cell system and method of operation in which the fuel cell system has a
fuel cell unit with anode and cathode, a media flow path for supplying substantially
pure hydrogen to the anode, a media flow path for the cathode, an anode exhaust-gas
flow path and a cathode exhaust-gas flow path. A fan for supplying air to the cathode
is provided in the flow path of the cathode, and a catalytic burner is arranged
in the cathode exhaust-gas flow path. The anode exhaust-gas flow path opens into
the catalytic burner and/or into the cathode exhaust-gas flow path upstream of
the catalytic burner. The combined, catalytically converted fuel cell exhaust-gas
flow is passed into an expansion machine.