A process and an apparatus for the continuous ozonization of unsaturated organic compounds in the presence of water, wherein(a) the fresh charge mixture of unsaturated compounds to be ozonized is reacted in at least one first reactor in parallel flow with ozonic gas, which was previously used for ozonizing a previously partially ozonized charge mixture, and(b) simultaneously a previously partially ozonized charge mixture is reacted in at least one second reactor in parallel flow with fresh ozonic gas,and wherein, optionally, said at least two reactors contain at least two mixing sections for mixing the charged liquid and gaseous phases with each other where the hydraulic diameter of the mixing elements in the individual mixing section is reduced in the flow direction.