Olefin-polymerization catalysts

A process for preparing an olefin polymerization catalyst, in which at least one compound selected from the group which consists of acetates, chlorides and acetyl acetonates of a transition element belonging to group I b, IIb, IIIb, IVb, Vb or VIb of the Periodic Table of elements is brought into contact with at least one "acetyl" compound selected from the group consisting of acetic acid, acetic anhydride and the fluoracetic and chloroacetic acids and their anhydrides, the mixture thus obtained is heated to a temperature of 70.degree. to 100.degree. C for a time of 10 to 30 hours, the excess "acetyl" compound is eliminated to give a solid residue, this residue is dispersed in a first inert anhydrous non-polar solvent, part of the dispersion so formed is introduced into an inert anhydrous non-polar organic solvent identical with the first solvent or miscible with it, the quantity introduced being so small that the liquid medium thus obtained remains homogeneous, and at least one aluminum organometallic compound of the general formula Al.sub.n R.sub.y X.sub.(3n-y) is introduced into this latter medium, where R is an alkyl group and X is a halogen, and n and 1 and y is 1, 2 or 3, or n is 2 and y is 3 or 5, the molar ratio of the aluminum organometallic compound to transition element being from 3.7:1 to 1060:1.