Process for preparing ethylene copolymers in the presence of free-radical polymerization initiator at pressures in the range of from 160 MPa to 350 MPa and temperatures in the range of from 100° C. to 350° C. in a tubular reactor by copolymerizing ethylene, a bi- or multifunctional comonomer and optionally further comonomers, wherein the bi- or multifunctional comonomer bears at least two different functional groups, of which at least one is a unsaturated group, which can be incorporated into the growing polymer chain, and at least another functional group can act as chain transfer agent in radical ethylene polymerization, ethylene copolymers obtainable by such a process, the use of the ethylene copolymers for extrusion coating and a process for extrusion coating a substrate selected from the group consisting of paper, paperboard, polymeric film, and metal, with such ethylene copolymers.