The present invention relates to a process for the production of mixtures of di- and polyamines of the diphenylmethane series (MDA) containing less than 1,000 ppm of water and less than 200 ppm of aniline by reaction of aniline and formaldehyde in the presence of acid catalysts and subsequent separation of the acid catalyst and subsequent distillative separation of water and aniline in an at least a two-stage distillation including a flash evaporation and subsequent cooling.