Device and method for purifying a gas mixture to produce a concentrated gas, notably neon, starting from a mixture comprising neon, said device including, in a cold box housing a cryogenic purification circuit comprising, in series, at least one unit for purifying the mixture by cryogenic adsorption at a temperature between 65K and 100K and notably 65K, then a unit for cooling the mixture to a temperature between 25 and 65 K and then a unit for cryogenic distillation of the mixture to produce the concentrated liquid at the outlet of the cryogenic distillation unit, characterized in that the unit for cooling the mixture to a temperature between 25 and 65 K comprises at least one cryocooler that extracts thermal power from the mixture via a heat exchanger.