Polyethylene which comprises ethylene homopolymers and copolymers of ethylene with α-olefins and has a molar mass distribution width Mw/Mn of from 6 to 100, a density of from 0.89 to 0.97 g/cm3, a weight average molar mass Mw of from 5000 g/mol to 700,000 g/mol and has from 0.01 to 20 branches/1000 carbon atoms and at least 0.5 vinyl groups/1000 carbon atoms, wherein the 5-50% by weight of the polyethylene having the lowest molar masses have a degree of branching of less than 10 branches/1000 carbon atoms and the 5-50% by weight of the polyethylene having the highest molar masses have a degree of branching of more than 2 branches/1000 carbon atoms, a process for its preparation, catalysts suitable for its preparation and also fibers, moldings, films or polymer blends in which this polyethylene is present.