Abstract: In a process for purifying natural gas in which methanol is injected into the natural gas, the temperature of the mixture of natural gas and methanol is lowered to the absorption temperature, at which undesirable components present in the natural gas are absorbed by the methanol, and the natural gas thus purified is separated from the methanol, the natural gas is subject to a succession of purification stages, each of which incorporates methanol injection into the natural gas, circulation of the mixture at the absorption temperature, and separation of the natural gas from the methanol phase. The partially purified natural gas which leaves a stage other than the last stage enters the stage which follows it and the purified natural gas is obtained at the outlet of the last stage.