A wastewater purification apparatus includes an elongate tank, which has an inflow for feeding wastewater, a first vertical agitator with a first hyperboloid agitator body mounted on a vertical first agitator shaft and provided in a first treatment portion downstream of the inflow on the first narrow side, a second vertical agitator with a second hyperboloid agitator body mounted on a vertical second agitator shaft and provided in a second treatment portion downstream of the first vertical agitator, an aeration device with a fan for aerating wastewater received in the tank, a first drive device for rotating the first hyperboloid agitator body in a first rotation direction, a second drive device for rotating the second hyperboloid agitator body in a second rotation direction opposite the first rotation direction, and a decanter for discharging purified wastewater in a third treatment portion on a second narrow side opposite the first narrow side.