Abstract: A gas-liquid mixing process and apparatus, particularly applied to aeration, especially associated with activated sludge waste-water treatment, wherein complete, efficient mixing of the gas and liquid is achieved initially in a pre-mixing draft tube and secondly in an outer mixing vessel by imparting a turbulent, random generally outward and upward radial motion to the liquid and gas contents of the vessel. A portion of the contents of the vessel is withdrawn and recirculated through the pre-mixing draft tube substantially axially vertically situated within the outer mixing vessel. A lower end of the draft tube has a nozzle opening which produces a net flow which is an axially symmetrical radial jet of recirculating contents, thereby establishing the desired turbulent random motion. In the case of aeration in waste-water treatment, air or other oxygen-containing gas is introduced into the draft tube.