NOVELTY - The gas is dried and compressed in a series of compressors each connected to a cooler and a separator. It is then progressively cooled and partially liquefied by successive passes through a cryogenic exchanger which is cooled by at least one coolant fluid which is liquefied natural gas.    USE - Fractionating gas from pyrolysis to obtain a flow containing hydrogen and methane and a flow containing hydrocarbons with two or more carbon atoms.    ADVANTAGE - Using LNG as the coolant in the cryogenic exchanger allows cooling power that is otherwise lost during regasification of the LNG to make significant savings in refrigerants and energy to cool them.    DETAILED DESCRIPTION - The gas (1) is dried and compressed in a series of compressors (3, 10, 17, 24, 36) each connected to a cooler (4, 11, 18, 25, 37) and a separator (5, 12, 19, 26, 39). It is then progressively cooled and partially liquefied by successive passes through a cryogenic exchanger (62). The cryogenic exchanger is cooled by at least one coolant fluid which is liquefied natural gas (LNG).    The pyrolysis gas (1) is fractionated into a first flow enriched in hydrogen and methane, a second flow which is basically water and a third flow containing most of the other hydrocarbons with two or more carbon atoms, particularly ethylene and ethane. CO2 is eliminated if the gas contains too much for compression. The gas is then progressively cooled and partially liquefied by successive passes through a cryogenic exchanger (62) and separation in separators (44, 46, 49, 52, 55) into liquids (71, 48, 51, 54, 56) rich in hydrocarbons with two or more carbon atoms and gases (45, 47, 50, 53, 59) poor in C2 and greater hydrocarbons. Each passage through the cryogenic exchanger brings the gas to a lower temperature and allows the hydrocarbons to be more completely liquefied. The gas from the last separator (55) forms the desired first flow enriched in hydrogen and methane. This gas is reheated in the cryogenic exchanger and collected. A distillation column is fed at different levels with the liquids collected from previous stages and partially expanded to allow separation into a head gas rich in methane and a base liquid rich in ethylene and ethane. The head flow is reheated in the cryogenic exchanger and recycled upstream of the compressor whose inlet pressure is nearest to the column pressure, and the base flow is heated in the cryogenic exchanger and collected to form the third flow. The temperature of the LNG at the inlet to the cryogenic exchanger is between -89 and -160 degreesC. The cryogenic exchanger is fed with two LNG flows, one high pressure and one medium pressure, produced by expanding part of the high pressure flow to lower its temperature. The fraction of LNG used in the medium pressure flow depends on the temperature of the LNG, with the fraction rising when the temperature is higher.    An INDEPENDENT CLAIM is also included for an installation for carrying out the above process.    DESCRIPTION OF DRAWING(S) - The figure shows a principal schematic of the process.    Gas from pyrolysis (1)    Compressor (3)    Cooler (4)    Separator (5)    Compressor (10)    Cooler (11)    Separator (12)    Compressor (17)    Cooler (18)    Separator (19)    Compressor (24)    Cooler (25)    Separator (26)    Compressor (36)    Cooler (37)    Separator (38)    Separator (44)    Gas poor in hydrocarbons with two or more carbon atoms (45)    Separator (46)    Gas poor in hydrocarbons with two or more carbon atoms (47)    Liquid rich in hydrocarbons with two or more carbon atoms (48)    Separator (49)    Gas poor in hydrocarbons with two or more carbon atoms (50)    Liquid rich in hydrocarbons with two or more carbon atoms (51)    Separator (52)    Gas poor in hydrocarbons with two or more carbon atoms (53)    Liquid rich in hydrocarbons with two or more carbon atoms (54)    Separator (55)    Liquid rich in hydrocarbons with two or more carbon atoms (56)    Gas poor in hydrocarbons with two or more carbon atoms (59)    Cryogenic exchanger (62)    Liquid rich in hydrocarbons with two or more carbon atoms (71)