A process for producing ethylene is proposed in which an ethane- and oxygen-containing reaction input is formed and a portion of the ethane and of the oxygen in the reaction input is converted into ethylene and into acetic acid by oxidative dehydrogenation to obtain a process gas, wherein the process gas contains the unconverted portion of the ethane and of the oxygen, the ethylene and the acetic acid and also water and wherein the process gas is subjected to a water quench. It is provided that the water quench comprises introducing the process gas into a scrubbing column (10, 20, 30, 40, 50) into which in at least two different column portions respective aqueous, liquid scrubbing medium streams are introduced and run in countercurrent to the process gas. A corresponding plant (100) likewise forms part of the subject matter of the invention.