Butyl rubber (isobutylene–isoprene–rubber, IIR) was functionalized in solution with a nitroxide moiety taking advantage of the unsaturations present in the isoprene units of IIR, and was further grafted with maleic anhydride (MA) or styrene–MA (SMA) to produce IIR-g-MA and IIR-g-SMA. In one of the functionalization techniques used, the molecular structure of the IIR was preserved as the chain-breaking reactions are prevented from occurring. The resulting graft copolymers were tested as compatiblizers/impact modifiers blended with Nylon-6, and one of them was preliminarily tested as a coupling agent in the preparation of nanocomposites of IIR and an organo-clay. Blends of PA-6/IIR-g-MA exhibited a significant increase in impact resistance at increasing loads of the modified IIR, as well as a good rubber particle dispersion in the polyamide matrix. On the other hand, the performance of IIR-g-SMA as an impact modifier of PA, or as a coupling agent in the preparation of rubber-organoclay nanocomposites, is marginal.