An endoscope with a flexible endoscope shaft has an endoscope head arranged at its distal end. The endoscope head is a sleeve, open at both end faces. Functional units, such as an optical system, a working channel, an illumination and a cooling system for the illumination are accommodated in the endoscope head. The cooling system has a heat exchanger integrally formed with the sleeve in the latter which forms a closed cooling chamber for generating a coolant flow. The illumination, which is in the form of an external conductor plate supporting an illumination means, is arranged adjacent to the distal end wall of the heat exchanger, to discharge thermal energy via the end wall of the heat exchanger to the coolant flow. The external conductor plate is mechanically supported on, or has only a minimum distance from, the heat exchanger end wall.