Radiation‐induced copolymer grafting of acenaphthylene and maleic anhydride onto polyethylene or EVA film in the vapor phase was carried out and the effect of comonomer sorption on the grafting was studied. When polyethylene film was used as a backbone polymer, the sorption of the binary monomers during the grafting increased linearly as the grafting reaction proceeded. The marked increase was probably caused by the formation of a grafted layer. Particularly, the sorption of maleic anhydride was brought about by the existence of a grafted layer. In grafting onto EVA film, the content of maleic anhddride in the grafted copolymer increased with the increasing content of vinyl acetate in EVA. Continuous measurements of sorption of the comonomers onto EVA and grafted EVA films were carried out by use of an electrobalance. The distinctive feature of the sorption was that the equilibrium sorption of acenaphthylene or maleic anhydride onto the grafted EVA film increased and the diffusion constants for both comonomers decreased markedly with increasing percentage of graft. The copolymer grafting was explained from these results by assuming that the monomer molecules are supplied to the propagating chain ends mostly through a sorbed state on the polymer film.