The apparatus (1) for cooling a super-conductive machine (2)has at least two mutually thermally separated condenser cavities (18, 18') which are in thermal connection qith a single cold head (16) through thermal resistors (33,33'). The at least two condenser cavities are respectively in connection with respective connecting pipelines (20, 20') through collection containers (34,34') used for collecting liquid cooling fluid (k). The at least two condenser cavities are in fluid connection with an evaporator chamber (12) through connecting pipelines; and the at least two collection containers are designed that cooling fluid (k,k') can move through at least one collection container to the evaporator chamber (12) through the differential pressure between a first pressure p1 in the first collection container and a second pressure p2 in the second collection container; the pressure can be determined by means of a ratio of vapoured cooling fluid of heating devices (35,35') which can circularly run in at least one collection containers.