A continuous flow multistage aerobic wastewater sludge digestion system comprising at least two stages connected in series, each stage comprising one or more covered tanks, tank segments or compartments, each having an enclosed separate gas headspace, wherein the gas headspaces of each stage are connected in a specified sequence that may be identical to or different from the staging sequence followed by the sludge liquid. An oxygen containing gas stream, such as air or an oxygen enriched gas stream, is supplied to the headspace of each stage, and a means for aerating the sludge in one or more of the tanks, tank segments or compartments is provided to enhance the transfer of oxygen from the gas headspace into the sludge liquid for use by bacteria in digestion of the sludge. At least one stage of the sludge digestion system is operated at a thermophilic temperature above 50 C. and the flow of oxygen containing gas through the system can be cocurrent, countercurrent, or a mixture of both with respect to the flow of the liquid.