An NMR apparatus comprising a superconducting magnet coil system, in particular, an NMR spectrometer, with a cryostat which comprises an outer shell and a helium tank which contains the magnet coil system, and with an NMR probe head which is disposed in a room temperature bore of the cryostat and which contains a cooled RF resonator for receiving NMR signals from a sample to be examined and is cooled, together with the NMR probe head, by a cold head of a common, multi-stage, compressor-operated refrigerator, is characterized in that the cold head of the refrigerator is disposed in a neck tube, the upper end of which is connected to the outer shell of the cryostat and the lower end of which is connected to the helium tank in such a manner that the neck tube and the helium tank delimit a helium space, with at least one cooling circuit with thermally insulated transfer lines being provided between the helium space and the NMR probe head, wherein the cryogenic helium in the helium space is used as coolant for the cooling circuit. This produces an NMR apparatus which cools a plurality of elements at different temperature levels using only one single cryocooler to optimally utilize the cooling resources of the refrigerator.