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, resulting in sorption of ethylene and 0 to 90% of the methane by the sorption agent and in a gas stream comprising methane in an amount of 10 to 100% based on the amount of methane in the gas stream that is subjected to the sorption step; and a desorption step which comprises desorbing sorbed ethylene and optionally sorbed methane resulting in a gas stream comprising ethylene and optionally methane.