The invention relates to a process for recovering methane from a gas stream comprising methane and ethylene, comprising: a sorption step which comprises contacting the gas stream comprising methane and ethylene with a sorption agent which has a lower affinity for methane than for ethylene, wherein the gas stream comprising methane and ethylene also comprises a compound for which the sorption agent has a lower affinity than for methane and ethylene, resulting in sorption of ethylene and methane by the sorption agent and in a gas stream comprising the compound for which the sorption agent has a lower affinity than for methane and ethylene; a first desorption step which comprises desorbing part of the sorbed methane resulting in a gas stream comprising methane in an amount of 1 to 99.9% based on the amount of methane in the gas stream that is subjected to the sorption step; and a second desorption step which comprises desorbing sorbed compounds resulting in a gas stream comprising the desorbed compounds.