An NMR apparatus comprising an NMR magnet system disposed in a first cryocontainer (2) of a cryostat (9), and an NMR probe head (1), wherein the first cryocontainer (2) is installed in an evacuated outer jacket and is surrounded by a radiation shield (24) and/or a further cryocontainer (3), wherein a cooling device is provided for cooling the NMR probe head (1) and a cryocontainer (2, 3), which comprises a cold head (4, 4a, 4b, 4c) with several cold stages (12a, 12b, 12c, 18a, 18b, 18c, 19a), wherein one cold stage (12a, 12b, 12c, 18a, 18b, 18c, 19a) is connected to a heat-transferring device, and wherein a cooling circuit is provided between the cooling device and the NMR probe head (1), is characterized in that the cooling device is disposed in a separate, evacuated housing (6) which is positioned directly above the cryostat (9), wherein the heat-transferring device is inserted directly into suspension tubes (29a, 29c) of the cryocontainer (2, 3) and/or is in contact with the radiation shield (24). This effects a simple construction that is efficient for cooling an NMR apparatus.