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 X signifies fluorine, chlorine and/or (+NR3)0-1, wherein R is a substituted C1 to C6 alkyl group or an unsubstituted C1 to C6 alkyl group, an unsubstituted C6 to C10 aryl group or a substituted C6 to C10 aryl group or a C5 to C6 heteroaryl group, R1 signifies hydrogen, C1-8-alkyl or an alkyleneoxy radical of formula (la), - (- C2-3 alkylene - O -)q - H (la) R2 signifies hydrogen or hydroxy, m signifies 1, 2 or 3, q is of from 1 to 10, M signifies hydrogen or an alkali metal cation or an ammonium cation, the ammonium cation being a protonated tertiary amine or a quaternary ammonium cation, in a tanning bath, the tanning bath having a pH of from 6 to 10 at the beginning of tanning step.