Multistage process for the polymerization of one or more olefins of the formula CH.sub.2 .dbd.CHR, in which R is hydrogen or an alkyl, cycloalkyl or aryl group having from 1 to 10 carbon atoms, comprising:(A) a first stage of polymerization, in which a first olefin polymer is prepared in the presence of titanium catalyst or vanadium catalyst;(B) a treatment stage in which the catalyst used previously is deactivated and in which a metallocene compound is supported on the olefin polymer produced in stage (A); and(C) a second stage of polymerization in which one or more olefins are polymerized in the presence of the product obtained from stage (B).