A metal-oxygen battery system, in particular a lithium-oxygen battery system, includes at least one battery cell, in particular a lithium-oxygen cell, including an oxygen cathode, a metal anode, and a metal ion-conducting separator situated between the cathode and the anode. To increase the current carrying capacity, the battery system also includes a turbomachine system which is connected to the oxygen cathode in a gas-conducting manner and which may be switched over between a suction function and a blowing function, and/or an exhaust gas supply line for supplying a gas low in oxygen to the oxygen cathode. Also described is a corresponding operating method.