A cryostat (1) with a magnet coil system including superconductors for the production of a magnet field B0 in a measuring volume (3) has a plurality of radially nested solenoid-shaped coil sections (4, 5, 6) and which are electrically connected in series, at least one of which being an LTS section (5, 6) with a conventional low temperature superconductor (LTS) and at least one of which being an HTS section (4) including a high temperature superconductor (HTS), wherein the magnet coil system is located in a helium tank (9) of the cryostat (1) along with liquid helium at a helium temperature TL. The apparatus is characterized in that a chamber (11) is provided within which the HTS sections (4) are held having an internal portion with a sufficiently low pressure such that helium located therein at a temperature of TL is gaseous. The cryostat in accordance with the invention can be utilized to maintain HTS coil sections over a long period of time in a reliable fashion.