Continous process for grafting a polyolefin within a melt including a polyolefin of linear olefin containing from 2 to 8 carbon atoms, a graftable functional monomer and a radical-generator, in an extruder including at its exit a compression zone followed by a discharge zone, in which at least one antioxidant additive is introduced into the melt not later than before the latter enters the compression zone of the extruder.Stabilized grafted polyolefin obtained by means of this process.