Copolymers of ethylene with .alpha.,.beta.-unsaturated carboxylic acids are prepared at from 50.degree. to 250.degree. C. and from 500 to 5000 bar in a stirred autoclave having a length/diameter ratio greater than 5:1 by a process in which the monomer mixtures are fed into the autoclave in at least two part-streams, the first part-stream being passed into the autoclave at the beginning of the autoclave pipe and the second part-stream being introduced at a position which is a distance away from the beginning which corresponds to 25-50% of the total length and the amount of the .alpha.,.beta.-unsaturated carboxylic acids in the first part-stream is from 20 to 90% less than the average amount in the further part-streams and a peroxide polymerization initiator having a lower decomposition temperature, or a mixture of peroxide polymerization initiators having a lower average decomposition temperature, than that of the initiators in the further part-streams is passed in with the first part-stream.