Abstract: A process for the stereospecific polymerization of olefins is described, wherein the selected monomer is homopolymerized, or the selected monomers are copolymerized, by reacting the selected monomer or monomers in the presence of a catalyst consisting of an uranium .pi. - allyl compound represented by one of the formulae: ##EQU1## in which R.sub.1, R.sub.2, R.sub.3, R.sub.4 and R.sub.5, the same or different, may be hydrogen atoms, alkyl radicals having from 1 to 10 carbon atoms, aryl radicals having from 6 to 10 carbon atoms, cycloalkyl radicals having from 4 to 10 carbon atoms, and alkylaryl radicals; the dotted line indicates the possible delocalization of the valence electrons; X is an anion selected from among Cl.sup.-, Br.sup.- and I.sup.-; and n is an integer ranging from 1 to 3; and, optionally, a co-catalyst which is a Lewis acid, or a complex thereof with an ether, a tertiary amine or a phosphine.