Abstract: Improved process for the oxidation of organic substrates by means of 1O2, in which 3-90% strength H2O2 is added to organic substrates which are soluble in water or in organic solvents miscible with water and which react with 1O2, in a water-miscible organic solvent, in water or in a mixture of water and water-miscible organic solvent in the presence of a heterogeneous or homogeneous catalyst, whereupon, following the catalytic decomposition of H2O2 to give water and 1O2, the oxidation of the substrates to give the corresponding oxidation products takes place, where, during the reaction, water is selectively removed from the reaction mixture by means of membranes.