Abstract: In a process for preparing polyethylene in tube reactors with or without autoclaves, where a free-radical initiator is introduced with or without cold ethylene into a flowing ethylene- and comonomer-containing medium, rotation is generated between two streams (61, 62) to be mixed at an angle (66) or by provision of a swirl element (20, 80) in the flow cross section (27, 28). In the region of a feed point (72, 81) for a free-radical initiator, there is provided a cross-sectional constriction (63, 67, 71) at which the free-radical initiator is introduced through an optimized off-center outlet opening (44) of an introduction finger (40) into the rotating flow (61, 62, 70).