In a process for distillatively removing ammonia and water from mixtures obtained in the preparation of polyamides which comprise a lactam and/or diamines, and, if appropriate, an aminonitrile and/or dinitrile, and also a cyclopentanone impurity in two stages: 1) the mixture is distilled at from 11 to 35 bar to give, as the top product T1, water, ammonia and cyclopentanone, and, as the bottoms B1, water, the lactam and/or diamines, and, if appropriate, the aminonitrile and/or dinitrile, and 2) T1 is distilled at from 11 to 35 bar to give, as the top product T2, ammonia and cyclopentanone, and, as the bottoms B2, water.