A syndiotactic propylene copolymer is obtained in high yields by copolymerization of propylene with small amounts of other olefins in the presence of a catalyst comprising a metallocene of the formula I ##STR1## in which M.sup.1 is titanium, zirconium, hafnium, vanadium, niobium or tantalum and an aluminoxane. This copolymer has a very high molecular weight, a very narrow molecular weight distribution, very high syndiotaxicity, advantageously low melting points and rubber-like behavior. Molded articles produced from the polymer are distinguished by high transparency, flexibility and tear strength. Their main areas of application are packagings of any type.