The paper reports a study of the effect of the addition of clay nanoparticles on melt rheology, phase structure, and non-isothermal crystallization process of isotactic polypropylene/hydrogenated oligocyclopentadiene (iPP/HOCP) system in quiescent conditions by DSC and under shear applied at different temperatures by SAXS. For both crystallization conditions, the addition of clay and/or HOCP shifts always the crystallization onset to lower values with respect to iPP. These results can be attributed to the diluent effect of HOCP that causes a decrease in the rate of nucleation and grow of the crystals, to the presence of segregated non-crystallizable phases/particles which hinder the transport of macromolecules chains toward the growing nuclei, and to the formation of beta iPP crystals and in the case of shear-induced crystallization to the presence of HPS which seems to reduce, mainly at low T (s), the amount of oriented polymer crystals, which are nuclei for the crystallization. At a given composition, the crystallization temperatures related at the crystallization under shear are always higher that those obtained by quiescent crystallization supporting the idea that the presence of extended chains in these samples act as nucleating agents favoring the crystallization process of iPP.