The invention comprises a catalyst support containing an &agr;-olefin polymer which is in the form of particles of mean size from 5 to 350 &mgr;m in which the pore volume generated by the pores of radius from 1,000 to 75,000 Å is at least 0.2 cm3/g. A catalyst usable for the polymerization of &agr;-olefins, including a compound containing at least one transition metal belonging to groups IIIb, IVb, IVb and VIb of the Periodic Table, bound in or on this support, is also described.