Tanned leather, skin or pelt is produced by non-metal tanning, comprising the step of tanning a bated hide, skin or pelt with a tanning agent (A), the tanning agent (A) being at least one compound of formula (I), wherein Hal signifies chlorine or fluorine, X signifies N or CR, Y signifies hydrogen, C1-8-alkyl, C1-4-alkyl-carbonyl, C-1-4-alkyl-sulphonyl or a radical of formula (Ia), or (Ib) —(—C2-3 alkylene-O—)q—H (Ib), R signifies hydrogen or chlorine, q is 1 to 10 and M signifies hydrogen, an alkali metal cation or an ammonium cation being a protonated tertiary amine or a quaternary ammonium cation, in a tanning bath having a pH of from 6 to 10 at the beginning of the tanning step.