A process is disclosed for separating the output from the reaction of EDDN or EDMN with hydrogen in the presence of THF, a catalyst, TETA or DETA, water, and optionally organic compounds having higher and lower boiling points than TETA or DETA. Hydrogen is removed, and the output is supplied to a distillation column DK1 in which an azeotrope, optionally comprising organic compounds with a boiling point lower than TETA or DETA, is removed from the top. A product comprising TETA or DETA is removed from the bottom and passed into a distillation column DK2, removing THF. A stream comprising TETA or DETA passes from the bottom of DK2. The DK1 azeotrope is condensed. Phase separation is induced by the addition of an organic solvent essentially immiscible with water, and the mixture is separated. The organic phase is recycled into DK1 and the water phase is discharged.