Abstract: Method of liquefying a mixture of gas rich in methane by performing an auxiliary cycle and a main cycle in which are used an auxiliary and a main refrigerating fluid of several components. In each cycle are performed the compression, cooling, liquefying and sub-cooling of the refrigerating fluids in counter-flowing relationship with themselves after expansion-vaporization in a heat exchanger. The gas to be liquefied is cooled in parallel with said main refrigerating fluid which has been pre-cooled in the auxiliary cycle. Pre-cooling of said gas is performed in an exchanger cooled by the refrigerating main fluid after its expansion-vaporization in said heat exchanging column of said main cycle and before its re-compression.