A process for the activation of a copper, zinc and zirconium oxide-comprising adsorption composition for the adsorptive removal of carbon monoxide from substance streams comprising carbon monoxide and at least one olefin wherein: (i) in a first activation step an activation gas mixture comprising the olefin and an inert gas is passed through the adsorption composition; and (ii) in a second activation step the adsorption composition is heated to a temperature in the range from 180 to 300° C. and an inert gas is passed through it, wherein the steps (i) and (ii) can each be performed several times.