Abstract: Gases, e.g., helium, are treated to freeze out impurities in the form of liquid and solids, and resultant gases are liquefied in a refrigerating unit. For automatic control of the freeze purification system, control of this process is responsive to two performance figures, namely, the liquefaction performance of refrigerating unit and the degree of impurities in the available crude gas. The purification process comprises an alternating sequence of purification phases A and regeneration phases B. The amount of gas used in regeneration phase B for liquefaction is additionally produced in purification phase A and intermediately stored in a medium-pressure buffer vessel. The sequence of purification phases A and regeneration phases B is continued up to a pressure P.sub.Mmax in the buffer vessel. Once this pressure is reached, the freeze purification system is regenerated; then, in an idle phase C, the pressure in the buffer vessel is reduced to P.sub.Mmin by liquefaction of the gas.