The invention relates to a process for the oxidation of organic compounds with oxygen in which, in a first step, the organic compound and at least some of the oxygen required for the oxidation are charged to a first reaction zone, where the first reaction zone is operated isothermally and back-mixed, and in a second step the reaction mixture from the first reaction zone is passed to a second reaction zone, where the second reaction zone is operated adiabatically. The invention further relates to a reactor for carrying out the process comprising at least one isothermal (3, 5) and one adiabatic (7) reaction zone which are arranged in a reactor jacket (8), where each isothermal reaction zone (3, 5) is configured in the form of a jet loop reactor and the adiabatic reaction zone (7) is configured as bubble column.