Abstract: The novel process for preparing ethylene copolymers by polymerizing ethylene with, as comonomer, up to 10% by weight, based on the total amount of the monomers, of a 1-olefin of the formula R—CH═CH2, where R is a straight-chain or branched alkyl radical having from 1 to 4 carbon atoms, is carried out in a polymerization reactor and in suspension with a dispersion medium at a temperature of from 20 to 100° C. and a pressure of from 2 to 20 bar, in the presence of a catalyst. The dispersion medium is then separated from the polymer. After carrying out the polymerization, but before removing the dispersion medium from the polymer, the suspension stream is partly evaporated, with the result that some of the wax formed in the polymerization is adsorbed onto the polymer and the resultant vapor stream is fed directly into the reactors after condensation or back into the process after distillative removal of the comonomer.