A process for working up reaction mixtures containing cyclohexanol and cyclohexanone, which have been obtained by oxidizing cyclohexane with molecular oxygen or gases containing molecular oxygen, in the liquid phase, at from 130.degree. to 200.degree. C. under a pressure of from 5 to 25 bars, working-up being effected by treatment with aqueous solutions of an alkali metal hydroxide and/or alkali metal carbonate in two stages, the fresh aqueous alkali metal hydroxide and/or alkali metal carbonate solution being fed to the second stage and the separated-off spent alkali being brought into contact with fresh reaction mixture in the first stage. The treatment in the first stage is carried out in the presence of inert gases and the inert gases are separated off before the second stage.