TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The waste water is water, waste water, aqueous, industrial, agricultural and production materials, industrial, agricultural and production gases, polluted air, gaseous and vent emissions, solid waste, materials of plant, animal or fossil origin, and/or solid, industrial, agricultural or production streams. A recuperable alkalinity control specie(s) selected from Ca, Zn, Al, Fe, Ni, Co and/or Cs is also provided. The treatment system is a multi step system and the sequence of steps is selected from sequential treatment steps, parallel treatment steps, parallel-sequential treatment steps, treatment steps in racetrack arrangement, and/or steps with recycling the waste water and the biomass among and between the steps. The operation mode of step(s) is continuous or batch operation, and/or continuous operation with flow equalization. The batch operation steps are filling, filling-stripping, reacting, reacting-stripping, settling and/or decanting steps. The biomass is selected from microorganisms selected from obligate aerobic, facultative aerobic, nitrifying, denitrifying, ferrous ion oxidizing, ferric ion reducing, anoxic, facultative anaerobic, sulfate reducing, methanogenic and/or obligate anaerobic. The oxidizing and/or reducing step(s) are conducted in different functional zones or same space in a single reservoir. The step of oxidizing terminal reducing agent(s) is selected from nitrification, anoxic, denitrification, facultative anaerobic, sulfate reduction, carbonate reduction, sludge conditioning, and/or biomass oxidation treatments. The step of reducing primary oxidizer is selected from oxygen enrichment, aerobic/anaerobic treatment, nitrification/denitrification treatment, anoxic treatment and/or facultative anaerobic treatment.Preferred Mediator Specie(s): The recuperable oxidation-reduction mediator specie(s) are metallic ions, metal containing species, oxyions, nonbiodegradable and insoluble inorganic constituents with variable oxidation-reduction states, nonbiodegradable and insoluble organic constituents with variable oxidation-reduction states, and/or redox ion exchange materials. The metallic ions and metal containing species include metals selected from Fe, Ni, Co, Mn, and/or V.Preferred Removal Of Nitrogen Oxyions: Step (b) is selected from facultative anaerobic treatment, sulfate reduction, carbonate reduction, sludge conditioning and/or biomass oxidation treatment. EXAMPLE - None given.