Hydrothermal oxidation of organic compounds, optionally with oxidizable inorganic compounds, is contained in an aqueous effluent. The aqueous effluent is injected within a tubular reactor and brought to supercritical pressure, and temperature is increased to a supercritical temperature, without any intermediate decrease in temperature, by introducing sufficient amounts of oxidizing agent within the tubular for totally oxidizing the organic compounds, and optionally for partly oxidizing oxidizable inorganic compounds. The oxidizing agent is introduced in a fractionated way in several points increasingly located downstream, and the composition and/or the concentration of the organic compounds and/or oxidizable organic compounds within the effluent to be treated varies over time. Further, upstream from the tubular reactor where oxidation is carried out, the effluent's total chemical oxygen demand of the effluent to be treated is measured and monitored at more than 120 grams/liter (g/L) and less than 250 g/L prior to injecting the tubular reactor.