A process for grafting an anhydride of an unsaturated aliphatic diacid onto a polyolefin comprising:(a) passing molten polyolefin through at least two injection zones connected in series;(b) injecting, under grafting conditions, a portion of a solution comprising the anhydride, an organic peroxide catalyst, and an inert organic solvent into the molten polyolefin as it passes through each injection zone, and mixing same in each injection zone until the portion is at least partially grafted onto the polyolefin; and(c) passing the grafted polyolefin, in the molten state, into a devolatilization zone, and mixing same in said zone, under devolatilization conditions, until the grafted polyolefin is essentially devolatilized.