Process for the preparing high molecular weight polymers by polymerization of water-soluble, monoethylenically unsaturated moonomers and, if desired, crosslinkers, and, if desired, water-insoluble monoethylenically unsaturated monomers, in aqueous solution in the presence of polymerization initiators in a tubular reaction which at the end has a conical taper, the ratio of the diameter of the reactor (D1) to the diameter at the end of the conical taper of the reactor (D2) being from 2:1 to 25:1 and the angle between D1 at the beginning of the conical taper and the inner cone wall being >45.degree. and <90.degree., and discharge of the gelatinous reaction mixture from the reactor by injection of an inert gas.