There are disclosed olefin polymerization catalysts based on tetra(neophyl) zirconium and its reaction products with surface-hydroxylated oxides of metals of Groups II(a), III(a), IV(a) and IV(b) of the Periodic Table of the Elements, processes for their preparation, and processes for the polymerization of olefinic monomers employing such catalysts. Neophyl zirconium aluminate supported on alumina is disclosed as the preferred, most active catalyst. The polyolefins produced are linear high polymers of high crystallinity such as polyethylene and isotactic polypropylene. Diolefins are converted into rubber by use of the process employing the catalyst. Ethylene-propylene copolymer rubbers can also be produced by use of the catalysts.