Abstract: Waste water to be treated is introduced into an enclosed gas tight oxygenation chamber. An oxygen-containing gas is also introduced into the oxygenation chamber, at a pressure higher than atmospheric pressure, such that oxygen from the gas is dissolved in the waste water in a quantity higher than the saturation concentration value of oxygen in the waste water at atmospheric pressure, thereby superoxygenating the waste water. The thus superoxygenated waste water, maintained at such pressure higher than atmospheric pressure, is then passed into an enclosed gas tight filtering chamber which is separate from the oxygenation chamber and which is also maintained at such pressure higher than atmospheric pressure. No other oxygen, other than the oxygen dissolved in the waste water, is introduced into the interior of the filtering chamber.