In a process for dehydration/fractionation of a wet natural gas containing heavy constituents and light constituents, In the presence of methanol, aqueous liquid phases are combined and the resultant combined aqueous liquid phase contacted with the first part of the gas to be scrubbed, which carries along the major part of the methanol, which allows to collect practically pure water. Before this step, all or part of one or both of the aqueous liquid phases and/or all or part of the aqueous liquid phase from a washing zone is sent to a distillation stage where practically pure methanol is collected at the top and a methanol-depleted aqueous liquid phase is collected at the bottom prior to being sent back to the first stage or used for the washing stage.