A catalyst formed by the reaction of a magnesium alkoxide dispersion having a particle size of from 100 to 3000 nm with a compound of a metal selected from the group comprising titanium, zirconium, vanadium and chromium and then with a chlorine-containing organoaluminum compound possesses a very good hydrogen responsiveness and a high activity even in the presence of molecular-weight regulators such as hydrogen. The catalyst is therefore outstandingly suitable for the production of low molecular-weight polyolefins. The catalyst makes possible the production of waxes having a reduced residual ash content. The large particle diameter and the low fines content of the polymer powder produced by suspension polymerization with this catalyst enables easy removal of the suspension medium and drying. The catalyst is furthermore advantageously used in solution polymerization and, because of the large particle diameter, in gas phase polymerization for producing low molecular-weight poly-1-olefins.