Abstract: The olefin polymerization catalyst comprises a supported transition metal, magnesium and halogen; the support comprises aluminum phosphate and at least one oxide of silica or alumina. The catalyst is formed by impregnating the support with a liquid complex formed by reacting a magnesium compound and a transition metal compound, which can contain either oxygen or halogen, and then precipitating the complex on the support with an organoaluminum compound which may be halogenated. The catalyst is used with an organometallic cocatalyst.

Abstract: Process for the polymerization of olefins, in which at least one olef in is placed in contact with a catalytic system comprising:(a) a solid catalytic complex based on magnesium, on transition metal and on halogen, and(b) an organometallic compound of a metal from groups IA, IIA, IIB, IIIA and IVA of the Periodic Table,the said solid catalytic complex (a) being prepared by reacting, in a first step, at least one magnesium compound with at least one compound of a transition metal from group IVB or VB of the Periodic Table until a liquid complex is obtained, by treating the said liquid complex, in a second step, using a halogen-containing organoaluminium compound, in order to precipitate the liquid complex as a solid catalytic complex, by separating, in a third step, the solid catalytic complex precipitated and by treating, in a fourth step, the separated solid catalytic complex obtained after the third step using a halogen-containing organoaluminium compound of general formula AlR.sub.n X.sub.3-n.