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 a formula (I), wherein X signifies fluorine or chlorine, and/or (+NR3)0-1, wherein R is a substituted or unsubstituted C1 to C6 alkyl group, a substituted or unsubstituted C6 to C10 aryl group or a C5 to C6 heteroaryl group, R1 signifies hydrogen, C1-8-alkyl or an alkyleneoxy radical of a formula (Ia), —(—C2-3 alkylene-O—)q—H (Ia), R2 signifies substituted or unsubstituted C2 to C8 alkylenesulphonic acid, substituted or unsubstituted C2 to C8 alkylenecarboxylic acid or an alkyleneoxy radical of formula (Ib), —(—C2-3 alkylene-O—)m—Y (Ib) or an alkylene sulfonyl alkyleneoxy radical of formula (Ic), —(—C2-3 alkylene-O—)p—C2-3 alkylene- SO2CH2O—Y (Ic), m signifies 1 or 2, p signifies 0 or 1, q is of from 1 to 10, Y signifies hydrogen or —SO3M, 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.