Abstract: A method for producing .alpha.-olefin polymers is provided. According to this method, particularly the catalyst stability is improved, resulting in polymers having a higher crystallinity, a narrower range of molecular weight, improved shape of polymer particles with a higher yield per a solid product component and per a transition metal component of the catalyst. Said catalyst is obtained by reacting a trivalent metal halide with a hydroxide, an oxide, a carbonate of a divalent metal, a double compound containing any of these compounds or a hydrate of a compound containing a divalent metal to form a solid product (I); reacting said solid product with one or more electron donors and one or more electron acceptors separately or simultaneously each in one to 10 steps but using TiCl.sub.