Tanning agents can be prepared by reacting at least one aldehyde of formula I, with at least one further identical or different aldehyde of formula I, where Z is a single chemical bond, unsubstituted or substituted C1-C12-alkylene, unsubstituted or substituted C5-C12-cycloalkylene or unsubstituted or substituted C6-C14-arylene, the reaction being carried out in the presence of an acidic catalyst and in the presence of at least one further carbonyl compound of formula II where R1 to R4, independently of one another, are hydrogen, unsubstituted or substituted C1-C12-alkyl, unsubstituted or substituted C3-C12-cycloalkyl, unsubstituted or substituted C7-C13-aralkyl or unsubstituted or substituted C6-C14-aryl, with the proviso that, where Z is a single chemical bond or a radical without a-hydrogen atoms, at least one further aldehyde of the formula I, in which Z contains α-hydrogen atoms, or at least one further carbonyl compound of formula II is present.