A method for producing a graft polymer comprises the steps of: a) irradiating a base polymer with an electron beam or a source of γ-radiation, b) contacting a grafting solution with the base polymer, wherein the grafting solution contains at least one oxygen scavenger and at least one graft monomer selected from the group consisting of styrene and styrene derivatives, and c) graft polymerizing the mixture of the base polymer and the grafting solution obtained in step b).