Abstract: The invention relates to a method for producing a poly-1-olefin by polymerisation of a 1-olefin of the formula R4CH?CH2, in which R4 is hydrogen or an alkyl radical having from 1 to 10 carbon atoms, in suspension, in solution or in the gas phase, at a temperature of from 20 to 200° 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 transition-metal compound of titanium, zirconium, vanadium or chromium with a gelatinous dispersion of the magnesium alkoxide in an inert hydrocarbon.