Multistage process for the polymerization of olefins CH.sub.2 .dbd.CHR, where R is hydrogen or an alkyl, cycloalkyl or aryl radical with 1-10 carbon atoms, comprising two stages of polymerization. In a first stage, in the presence of a titanium or a vanadium catalyst and working in one or more reactors, an olefinic polymer with particular values of porosity is prepared; in a second stage, in the presence of the said porous polymer and a metallocene compound and/or their reaction products, one or more olefins, that are equal to or different from those polymerized in the first stage, are polymerized in one or more reactors.