A biofilter system of the present invention utilizes an Alternating-Aerobic-Anoxic (AAA) process in a single reactor to provide efficient and cheap removal of carbonaceous materials, nitrogenous materials, and/or mixtures thereof from aqueous waste. The biofilter system of the present invention is particularly suitable for treating aqueous waste from aquaculture, industrial processes and animal husbandry. The biofilter system includes: a main biofilter chamber containing therein aerobic and anaerobic bacteria without physical separation; an inlet port and an outlet port connected to the main biofilter chamber; and a means for oxygenating the aerobic and anaerobic bacteria in the main biofilter chamber, including means for timing the oxygenation of the aerobic and anaerobic bacteria to provide alternating periods of high-oxygen conditions and anoxic conditions.