Abstract: The invention relates to methods and systems for liquefaction of gases whose critical temperature is lower than the ambient temperature, such as, for instance, natural gas, air, nitrogen, oxygen, etc. Compressed to supercritical pressure gas to be liquefied is cooled by external refrigerator means to a predetermined final temperature that is lower than the saturation temperature of the liquefied gas, and then is throttled to a subcritical pressure. As a result, all gas supplied to the apparatus is liquefied without generating any flash gas, and controlled rate of liquefied gas subcooling is achieved. Three modifications of the apparatus for gas liquefaction employing refrigerator means, based on reversed gas cycles, are introduced. Another modification of the apparatus with refrigerator means applying open air cycle and Compressed Air Energy Storage (CAES) is also developed.