Process for separating esters of vinyl alcohol from a gas stream comprising from 70 to 99.5% by weight of ethylene and from 0.5 to 30% by weight of esters of vinyl alcohol being at a pressure in the range of from 0.5 MPa to 10 MPa and a temperature in the range of from 5° C. to 50° C. comprising the steps of a) cooling the gas stream in a first heat exchanger by means of a cooling medium to a temperature of from −5° C. to 40° C.; b) withdrawing the not condensed part of the gas stream from the first heat exchanger and transferring it to a second heat exchanger; c) cooling the gas stream in the second heat exchanger to a temperature of from −20° C. to 5° C.; d) withdrawing the not condensed part of the gas stream from the second heat exchanger, reducing the pressure of the gas stream to from 0.5 MPa to 3 MPa and transferring it to a separation vessel; e) withdrawing the not condensed part of the gas stream from the separation vessel and transferring it as cooling medium to the second heat exchanger; and f) withdrawing the cooling medium as ethylene gas stream with a reduced content of esters of vinyl alcohol from the second heat exchanger, and process for copolymerizing ethylene and esters of vinyl alcohol in the presence of free-radical polymerization initiators at pressures in the range of from 110 MPa to 500 MPa and temperatures in the range of from 100° C. to 350° C. in a continuously operated polymerization apparatus comprising such a process for separating esters of vinyl alcohol from a gas stream comprising from 70 to 99.5% by weight of ethylene and from 0.5 to 30% by weight of esters of vinyl alcohol.