The present invention relates to a cooling device for a jet engine having an axial compressor with several compressor stages including a rotor with rotor blades, a stator with stator vanes and an annulus. In order to reduce the temperature of the components at the outlet of the high-pressure compressor by simple measures and hence to increase the efficiency of a jet engine, a slot-like branch opening surrounding the rotor for a cooling airflow diverted from the main airflow into a first cavity upstream of the rotor is provided upstream of the last compressor stage of the axial compressor, with passage openings being arranged in the rotor for passing on the diverted cooling airflow from the first cavity into a second cavity downstream of the rotor.