The present invention relates to a process and apparatus for oxidizing an aqueous medium, which contains organic and/or oxidizable inorganic substances, at an increased temperature and an increased pressure for reducing the chemical oxygen demand of the aqueous medium to a predetermined desired level. The aqueous medium is introduced into a tubular reactor with an oxygen-containing medium. The tubular reactor contains a mechanism for dispersing bubbles of gaseous oxygen. The reactor contains sections through which the mixture of aqueous medium and oxygen containing medium serially flows. A degree of back-mixing in any one of the sections is equal to or less than the degree of back-mixing of an upstream section and the farthest downstream section has a smaller degree of back-mixing than the farthest upstream section.