Abstract: A process for preparing polypropylene compositions having high impact strength at low temperatures is disclosed in which the reaction is catalyzed by Ziegler-Natta/metallocene hybrid catalysts by the in-situ polymerization of one or more olefins of the formula CH2?CHR, in which R is hydrogen or an alkyl, cycloalkyl or aryl group having from 1 to 10 carbon atoms, and more specifically comprises preparing an olefin polymer by Ziegler-Natta catalyst components of the titanium or vanadium/metallocene hybrid catalysts while the metallocene components are inactivated beforehand by catalyst inactivators; and polymerizing one or more olefins in the presence of the above olefin polymer, followed by a reactivation of the metallocene components.