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 step (i) and (ii) can each be performed several times.