Hexamethylenediamine and aminocapronitrile are simultaneoussly produced by hemihydrogenation of adiponitrile, which includes a stage of separation of the hexamethylenediamine from the hydrogenate by distillation of the hexamethylenediamine, the distillation of the hexamethylenediamine being carried out from the hydrogenate containing a free acid and/or an alkali metal or ammonium acid salt, whereby a top fraction A recovered at the column top of the stage of distillation of the hexamethylenediamine is essentially crude hexamethylenediamine and a small amount of THA; the amount of THA (tetrahydroazepine) present in the crude hexamethylenediamine constitutes a small proportion of the THA present in the hydrogenate.