Multi-stage process for the polymerization of olefins CH₂CHR, where R is hydrogen or a C₁-C₁₀ alkyl, cycloalkyl or aryl radical, comprising: (I) a first polymerization stage carried out in the presence of a catalyst comprising the product of the reaction between an alkyl-Al compound and a solid component comprising at least one compound of transition metal M¹ not containing M¹- bonds, thus obtaining a porous polymer, (II) a treatment stage, wherein said porous polymer is contacted with a compound capable of deactivating the catalyst used in stage (I) and with a late transition metal complex; and (III) a second stage of polymerization, carried out in the presence of the product obtained from treatment stage (II).