The invention relates to esterquats which can be obtained by reacting di- or trialkanolamines with a mixture of fatty acids and polycarboxylic acids, and the esters obtained in this manner are then quaternized with an alkylating agent, wherein the di- or trialkanolamines correspond to formula (I), in which R1 and R2 independently of one another represent hydroxyalkyl groups with 1 to 20 carbon atoms, hydroxyalkenyl groups with 2 to 20 carbon atoms and 1, 2, or 3 double bonds, or addition products of 1 to 20 mol ethylene oxide on a hydroxyethyl group and R3 represents hydrogen, an alkyl group with 1 to 20 carbon atoms, an alkenyl group with 2 to 20 carbon atoms and 1, 2, or 3 double bonds, a hydroxyalkyl group with 1 to 20 carbon atoms, a hydroxyalkenyl group with 2 to 20 carbon atoms and 1, 2, or 3 double bonds, or addition products of 1 to 20 mol ethylene oxide on a hydroxyethyl group; the fatty acids correspond to formula (II), R4—COOH  (II) in which R4 represents an aliphatic, linear, or branched hydrocarbon group with 5 to 29 carbon atoms and 0, 1, 2, or 3 double bonds; and the polycarboxylic acids correspond to formula (III), in which Y represents a carbon atom or a saturated or unsaturated aliphatic hydrocarbon group with 2 to 5 carbon atoms, said group optionally having one or more hydroxyl groups, and X represents hydrogen or a hydroxy- or carboxylic acid group. The invention also relates to the use of said esterquats as collectors for the flotation of non-sulfidic minerals.