Abstract: Graft polymers which comprise 20 to 99.9% by weight of an ethylene copolymer (base polymer) and 0.1 to 80% by weight of a graft component. The base polymer includes 30% to 95% by weight of ethylene and (1) 5% to 70% by weight of vinyl esters of saturated aliphatic C.sub.2 - to C.sub.18 -monocarboxylic acids or (2) 4% to 50% by weight of vinyl esters of saturated aliphatic C.sub.2 - to C.sub.18 -monocarboxylic acids and 1% to 20% by weight of linear or branched C.sub.3 - to C.sub.18 -monoolefins. Graft components are N-substituted alpha,beta-unsaturated dicarboxylic acid imides, dicarboxylic acid amides, dicarboxylic acid half-amides, or ammonium salts of the half-amides. The graft polymers are employed for improving the flow properties of paraffin-containing mineral oils, mineral oil distillates, and middle distillates.