An air supply system for a gas turbine engine including a first duct which is connected or capable of being connected to a first compressor bleed air supply of a gas turbine engine; a second duct which downstream of the first compressor bleed air supply is connected or capable of being connected to a second compressor bleed air supply of the gas turbine engine; a nozzle by way of which air from the second duct is capable of being blown into the first duct; and an exhaust air duct having an opening which downstream of the nozzle is disposed in the first duct in such a manner that air blown by way of the nozzle into the first duct can flow out of the first duct through the opening into the exhaust air duct. A gas turbine engine and an aircraft are furthermore provided.