Disclosed is a polymer of average molecular weight ranging from 400 to 20,000 comprising amino substituted groups in its molecule and resulting from the reaction of at least one compound with a primary amine function having 1 to 60 carbon atoms with an unsaturated polyester resulting from the condensation of an unsaturated aliphatic dicarboxylic compound, comprising at least one ethylenic unsaturation in the alpha position of one of the carboxyl groups, with at least one epoxidated compound having 4 to 62 carbon atoms chosen from ethers and esters of epoxyalcohols and esters of epoxyacids.Also disclosed is a middle distillate composition having a distillation range from 150.degree. to 450.degree. C. and comprising a minor proportion, preferably from 0.001 to 2% in weight, of at least one of the polymers defined hereinabove.