Process for the conversion of plastics to olefins comprising the following steps: A) gasification of the plastics to synthesis gas by reaction of the plastics with pure oxygen; B) catalytic conversion of the synthesis gas produced in stage A) to methane in at least three successive stages, in each of which hydrogen is added; C) catalytic conversion of the methane produced in stage B) into olefins by the oxidative coupling reaction of methane; and D) separation of the olefins produced in stage C) from other compounds present in the reaction mixture of said stage C).