The invention relates to a method and a device for purifying liquid effluents, in which water is separated from substances by performing, in a single vertical enclosure (3), a vertical bubbling in the effluents fed at a flow rate d. The enclosure has a free surface and includes at least two compartments (4, 5, 6, 7) communicating together for enabling a circulation between the compartments successively from the top to the bottom and from the bottom to the top between the lower portion thereof and a medium level at a flow rate D at least three times higher than the flow rate d. The supernatant phase is continuously discharged and a hydraulic or gaseous chemical oxidation of said effluents is simultaneously carried out in the same enclosure, the chemical oxidation rate and the bubble flow rate and size being selected in order to progressively obtain a separation of the solid/liquid and liquid/liquid phases at the surface of the enclosure for obtaining a COD below a predetermined threshold.