Abstract: Atactic waxes and method for preparing same by polymerization of polyolefin alone or in combination with other monoolefins of the formula CH.sub.2 = CHR in which R is hydrogen or an alkyl radical having from 2 to 8 carbon atoms in which the polymerization is carried out at low pressure and in a hydrocarbon solvent in the presence of a catalyst formed of the product of the reaction of magnesium or a compound thereof, a compound of a transition metal selected from the sub-groups IVa, Va and VIa of the periodic classification of elements and an alkyl halide, and a co-catalyst in the form of an organometallic compound of a metal selected of groups II and III of the periodic classification of elements.