Procedure and applying plant (H2 / He)-CBS-RB & J-T thereof destined to gas liquefaction, based on • the synergic use of two cycles, Joule-Thomson and Reverse Bryton, abbreviated by J-T and RB, respectively, operated by the gas to be liquefied and He, respectively, • precooling of the gas to be liquefied with the help of the ultra-low temperature refrigeration, abbreviated by ULTR, generated by coabsorbent truncated refrigeration cycles, abbreviated by CBS, connected in cascade and supplied by the sink source of a power cycle operating in condensation and by a heat source of low temperature and free, aiming of the condensing heat of the power cycle, • multi-stage compression, differentiated in the J-T cycle for Hi, as compared to the other gases, e.g., ex. He, Ne, N2, O2, Ar, CH4, etc. and of He in the RB, where the conversion of the compressed gas superheat in mechanical work, abbreviated by TWRC, is practiced, using ULTR in the Rankine Recovery Cycle, abbreviated by RRC, • the final cooling of the gas in the j-T cycle, its expansion and the obtainment of the useful liquefied gas fraction and • selfinduction of a superconductibility state in its electrical elements conducting electricity, belonging to the electrical driving system of e.g. compressors, by achieving them out of adequate materials and their continuous cooling by a small amount of liquefied gas to temperatures below their critical temperatures in order to eliminate completely the Joule effect dissipative electrical losses and increase liquefaction efficiency.