A process (100) is proposed for the production of one or more olefins, in which a reaction feed containing oxygen and one or more paraffins is formed and in which a part of the oxygen in the reaction feed is reacted with a part of the one or more paraffins to form the one or more olefins by an oxidative process, to obtain a process gas, the process gas containing at least the unreacted part of the one or more paraffins and oxygen, the one or more olefins, one or more acetylenes, carbon dioxide and water. The process comprises subjecting the process gas or a gas mixture formed using at least a part of the process gas partially or completely to a condensate separation (2), a compression (3), an at least partial removal (4) of the oxygen and acetylene(s) and to one or more stages of a carbon dioxide removal (5) in the order given herein, wherein the at least partial removal (4) of the oxygen and of the acetylene(s) is performed at the same time and by a catalytic conversion using a catalyst comprising copper oxide or ruthenium, and wherein the catalytic conversion is performed at least in part in the form of a hydrogenation. A corresponding plant is also the subject of the present invention.