In a process for preparing ethylene-vinyl acetate copolymers in which a mixture of ethylene and vinyl acetate is polymerized continuously in the presence of free-radical polymerization initiators and, if desired, molecular weight regulators in a cooled tube reactor at a pressure in the range from 1000 to 3500 bar, and the poly-merization initiator is added at the beginning and at two or more points along the tube reactor, and temperature changes in the reaction mixture along the tube reactor, between the first temperature maximum and the last addition of the polymerization initiator, are within a range of not more than 20° C.