A process is provided for preparing a catalyst support for polymerizing &agr;-olefins comprising the steps of: (i) reacting, in the presence of a first electron donor, a chlorine-containing organic compound and a prior mixture of an alkylmagnesien and an aluminoxane and/or aluminosiloxane and/or alkylaluminum and, optionally, a second electron donor; and (ii) activating a product from step (i) in suspension in an inert liquid by means of an activation electron donor, together with the support thus obtained, a catalyst for polymerizing &agr;-olefins, comprising this catalyst support and a group IV transition metal halide, and a process for polymerizing &agr;-olefins, particularly propylene, comprising contacting the &agr;-olefin with the catalyst.