The effect of multiwalled carbon nanotubes (MWNT) on the course of reactive-extrusion-free-radical grafting of trans-ethylene-1, 2-dicarboxylic acid onto linear low-density polyethylene (LLDPE) and ethylenepropylene copolymer (c-PP) containing ≈7 wt.% ethylene units was studied. The extrusion reactor was the material cylinder of the twin-screw extruder TSSK-35/40 (screw diameter 35 mm; length/diameter ratio = 40; 10 independent heating zones). It was found that the extent of the influence of MWNT depends on their concentration and on the PO character. It is shown that monomer grafting efficiency can be improved with a MWNT concentration of ≈0.05 wt% in the reactive system. In free-radical grafting of the cross-linkable LLDPE, the MWNT ( ≥ 0.1 wt%) were shown to inhibit the concurrent process of macromolecular cross-linking; in the case of c-PP, which predominantly undergoes degradation during functionalization, the concurrent reactions were observed to accelerate catalytically. In the case of polyamide 6/LLDPE blends, the MWNT promote the strengthening of melt flow junctures that formed during the filling of the die-mold cavity.