Mineral oil compositions with trace portions of additives contain as additive a comb polymer containing ester linkages, either based on a) ethylene-vinylester copolymers modified by hydroxy groups or glycidyl groups with molecular mass weight averages from 3000 to 50000 and an ethylene portion of 50 to 90 mass %, and b) partially imidated and/or partially esterified maleic anhydride copolymers, wherein in the comb polymer based on a) and b) the modified ethylene-vinylester copolymer component is connected by means of ester linkages to the partially imidated and/or partially esterified maleic anhydride copolymer component, or a comb polymer containing ester linkages based on c) ethylene-vinylester copolymers modified by acid and/or acid anhydride groups with molecular mass weight averages from 3000 to 50000 and an ethylene portion of 50 to 90 mass %, and d) polyalcohols partially esterified with C12-C40-monocarboxylic acids wherein in the comb polymer based on c) and d) the ethylene-vinylester copolymer component modified by acid and/or acid anhydride groups is connected by means of ester linkages with the polyalcohol component partially esterified with C12-C40-monocarboxylic acids. The mineral oil compositions are suitable as flowable media to be transported at low temperatures and as mineral oil fuels with high lubricity and flowability.