A process for preparing polyethylene which comprises ethylene homopolymers and/or copolymers of ethylene with 1-alkenes and has a molar mass distribution width Mw/Mn of from 5 to 30, a density of from 0.92 to 0.955 g/cm3, a weight average molar mass Mw of from 50000 g/mol to 500 000 g/mol and has from 0.01 to 20 branches/1000 carbon atoms and a z-average molar mass Mz of less than 1 million g/mol.