Disclosed are polymers of average molecular weight ranging from 400 to 20,000 comprising thiosubstituted groups per molecule and resulting from the reaction, in the presence of an addition catalyst, of at least one compound with a thiol function, having 1 to 60 carbon atoms per molecule, with an unsaturated polyester resulting from the condensation of an aliphatic epoxide with an unsaturated aliphatic dicarboxylic compound comprising at least one ethylenic unsaturation in the alpha position of one of the carboxyl groups. Also disclosed are middle distillate compositions having a distillation range from 150.degree. to 450.degree. C. and comprising a minor proportion, preferably from 0.001 to 2% by weight, of at least one of the polymers defined hereinabove.