A combustion system comprising a burner and a combustion chamber, is connected by way of a line to a membrane unit having a high-temperature membrane for extracting the combustion oxygen from the air, the membrane unit having a feed line for a flushing gas on the permeate side. The combustion system further comprises a circulation element for recirculated flue gas, a heat exchanger being disposed upstream of the membrane unit inside the flue gas line. Disclosed is a method for operating this combustion system, in which carbon-containing fuel is burned in an oxygen-flue gas atmosphere, and in which the oxygen for combustion is produced from air by means of a membrane unit comprising a high-temperature membrane, and in which the flue gas is in part recirculated. Disclosed are the steps of first cooling the recirculated flue gas, optionally for a flue gas scrubbing process, subsequently reheating the cooled flue gas to ensure the necessary operating temperature of the membrane, the heating energy being extracted by way of a heat exchange with the flue gas having the corresponding temperature level of the combustion process, and feeding the flue gas heated in this manner to the membrane unit as a flushing gas.