The influence of a new processing additive (particles of organically modified nanoclays) on the processibility of polyolefins in extrusion is studied. The equipment used includes an Instron capillary rheometer with two types of dies, namely capillary dies and special annular dies (Nokia Maillefer wire coating crosshead) attached to the rheometer. Ziegler Natta and metallocene polyethylenes and one polypropylene were tested using these two pieces of equipment. It was found that the nanoclay additive had a significant effect on the extrudate appearance of polyethylene. It eliminates surface melt fracture and postpones the critical shear rate for the onset of gross melt fracture to significantly higher values depending on resin type, temperature, and additive concentration (typically 0.05 to 0.5 wt%). To explain the possible mechanism for the effect of the additive on the processibility of the resins, shear and extensional rheological measurements were carried out for the pure resins as well those loaded with the nanoclay additives. It seems that the presence of nanoclays suppresses the development of extensional stresses to such high levels that can cause melt fracture phenomena. Finally, it was found that the combination of nanoclays with traditional processing aids such as fluoropolymers produce an enhanced processing aid that can increase the critical shear rates for the onset of melt fracture to levels much higher than the individual constituents when they are used independently.