PURPOSE: To realize a highly efficient and a highly reliable cryogenic refrigerating system by a method wherein Gifford Macmaphon refrigerating cycle is combined with a magnetic refrigerating cycle and single circulating loop employing helium gas of common operating fluid is constituted.

CONSTITUTION: When a high pressure valve 3 is opened, a low pressure valve 4 is closed and a magnetic field, applied on a cold heat accumulator 10A and generated by superconductive magnets 26, is reduced, the temperature of the cold heat accumulator 10A is reduced by magnetic refrigerating effect. Simultaneously, high-pressure helium gas flows from a compressor 2 into a cylinder 6 whereby a pressure in a room temperature space 16 above a displacer 8 increases from a low pressure PL to a high pressure PH. Next, when the displacer 7 is moved upward, helium gas in the room temperature space 16 dissipates heat through cold heat accumulators 8A, 9B, 10A and is cooled, then, moves to a chamber 17, an expansion chamber 18 and another expansion chamber 19. When the magnetic field, applied on the cold heat accumulator 10A, is reduced further, the helium gas, passing through the cold heat accumulator 10A through a pipeline 24, is cooled further more, then, is discharged out of the cold heat accumulator 10A and absorbs heat from a refrigerating load 29 in the part of a pipeline 25, then, enters the expansion chamber 19.