A cascade liquefier is an apparatus for liquefying air, oxygen, etc. A gas cannot be liquefied until it is brought to a temperature below its critical temperature. In the cascade liquefier the critical temperature of the gas is reached step by step, using a series of gases having successively lower boiling points. The first of these, which can be liquefied by compression at ordinary temperatures, is allowed to evaporate under reduced pressure; this produces a temperature below the critical temperature of the second gas, which can then be liquefied. This is similarly allowed to evaporate, and the step is repeated until finally the desired liquefaction is reached.