In the simultaneous irradiation procedure, sensitized W radiation is shown to be a complementary initiator to ionizing radiation for the grafting of monomers to polyolefins. Parameters influencing the yield of graft have been considered, including the role of sensitizer, solvent, and the type of monomer. These results indicate why difficulties have been experienced by previous authors in photografting monomers to polymers using analogous procedures. Grafting of styrene to cellulose acetate using ionizing radiation at low total doses is also reported. Difficulties associated with the poor grafting yield to gel beads as opposed to films are considered predominantly in terms of moisture content and swelling of the gel beads. The feasibility of using the polyolefins and cellulose acetate beads modified by the present grafting methods in reagent insolubilization reactions is discussed.