The preparation of amines of the formula (I): R1R2CH—N R3R4  (I) in which R1, R2, R3 and R4, independently of one another, are hydrogen, straight-chain or branched C1-C12-alkyl, C3-C12-cycloalkyl, C6-C10-aryl or C7-C11-aralkyl, takes place by catalytic, reductive amination of mixtures comprising carbonyl compounds of the formula (II) and/or alcohols of the formula (III) R1—C(═O)—R2  (II) R1—CH(OH)—R2  (III) which also comprise at least 50 ppm, based on the mixtures, of halogen, with nitrogen compounds of the formula (IV): H N R3 R4  (IV) with the abovementioned meanings for R1 to R4, in the presence of Co- and/or Ni-containing catalysts, which comprises carrying out the reductive amination additionally in the presence of solid acidic cocatalysts.