Carboxyl-containing copolymers of ethylene are prepared by polymer-analogous pyrolytic ester cleavage of copolymers consisting ofa) from 60 to 99.9 mol% of ethylene,b) from 0.1 to 40 mol% of C.sub.4 -C.sub.8 -tert-alkyl esters of copolymerizable C.sub.3 -C.sub.12 -carboxylic acids andc) from 0 to 20 mol% of further copolymerizable monomers by a method in which pyrolytic ester cleavage is carried out at from 150.degree. to 250.degree. C. in the presence of organic sulfonic acids, in the absence of a solvent and in the virtual absence of free radical initiators.