Method for concentrating an organic hydroperoxide mixture comprising a hydrocarbon and a hydroperoxide corresponding thereto comprises evaporating a first liquid mixture in a thin-film evaporation device followed by separation in a separation zone. Both the evaporation device and the separation zone operate at a low absolute pressure at a temperature lower than the thermal degradation temperature of the hydroperoxide to prevent thermal decomposition thereof. The process is particularly useful for concentrating an oxidation product made from the oxidation of cyclohexylbenzene.