Abstract: Gel-free ethylene/vinyl acetate copolymers with a high content of copolymerized vinyl acetate and a high Mooney viscosity are produced by carrying out the polymerization in solution in the presence of 20 to 45% by weight tert.butanol, based on the reaction solution, at temperatures of 50.degree. to 80.degree. C. and under pressures of 300 to 450 bar using azo compounds in a cascade of stirred reactors with an average residence time of the reaction solution in the reactor cascade of 5 to 9 hours and a conversion of 50 to 70% by weight, based on the vinyl acetate used. The ethylene/vinyl acetate copolymers produced by the process according to the invention may be used for the production of vulcanizates having improved mechanical properties.