The invention relates to a method for producing a poly-1-olefin by polymerization of a 1-olefin of the formula R.sup.4C.dbd.CH.sub.2, in which R.sup.4 is hydrogen or an alkyl radical having from 1 to 10 carbon atoms, in suspension, in solution or in the gas the gas phase, at a temperature of from 20 to 200.degree. C. and a pressure of from 0.5 to 50 bar, in the presence of a catalyst which consists of the product of the reaction of a magnesium alkoxide with a transition-metal compound (component a) and an organometallic compound (component b), whose component (a) has been produced by reacting a transitionmetal compound of titanium, zirconium, vanadium or chromium with a gelatinous dispersion of the magnesium alkoxide in an inert hydrocarbon. In accordance with the invention, the gelatinous dispersion is obtained by stirring, using a stirring element, or shearing, using a high-performance shearing tool, a suspension of a magnesium alkoxide powder having a mean particle size, expressed as the d.sub.50 value, in the range from 50 to 1000 um, in an aliphatic hydrocarbon in which the magnesium alkoxide particles are insoluble. The suspension has, before conversion into the dispersion, been subjected to heat treatment at a temperature in the range from 40 to 150.degree. C. over a period of from 10 to 100 hours.