A system for cryogenic storage and delivery of fuel, particularly for supplying an internal-combustion engine driving a motor vehicle, includes at least a cryotank having an inner reservoir for receiving the cryogenic medium, which inner reservoir is held in a heat-insulated manner in an outer reservoir, a coolable cooling shield between the inner reservoir and the outer reservoir of the cryotank, and a heat sink. As a thermal-energy storage device, the heat sink is in heat-transmitting contact with the cooling shield. A filling and removal device has at least one pipe penetrating the outer reservoir and leading into the inner reservoir. At least for the filling with or for the removal of cryogenic medium, the heat sink is in heat-transmitting contact with the pipe for the cryogenic medium, in order to reduce the entry of heat from the environment into the inner reservoir while emitting heat. The inner reservoir has a recess in which at least the heat sink and the pipe for the cryogenic medium are housed such that they are situated essentially within the circumferential contour of the inner reservoir.