A process for oxidation of oxidizable materials which are dissolved or suspended in a liquid phase. A contactor in the form of a porous membrane is used. The contactor is designed such that an oxidizing phase flows along one surface thereof while the phase to be oxidized flows along another surface. The oxidation is catalyzed by (i) a catalyst material which constitutes the porous membrane or is deposited in or onto a porous membrane support, or (ii) a catalyst material which is supplied to one or both of the feed streams comprising the oxidizing phase and the phase to be oxidized.