Abstract: The present invention relates to a process for the preparation of random copolymers of propylene with c2-c10&agr;-olefins, carried out in the presence of a catalyst comprising: A) A solid component comprising a titanium compound supported on mgcl2 in active form and an electron-donor compound; b) An alkyl-al compound, and c) An electron-donor compound selected from the group of 1,3-diethers. The copolymers obtained using the said process show, for an equivalent content of &agr;-olefin, a lower content of xylene-soluble fractions when compared with the copolymers obtained with the catalysts of the prior art.