Abstract: To purify untreated water, for example waste water, containing organic pollution, materials in suspension and nitrogen-containing pollution, reagents are added under conditions adapted to coagulate all of the materials in suspension, including colloidal materials, to form granular physical/chemical floc. Diluting water is added, preferably after the reagents, in a flowrate ratio of at least 2/1. The dilute flocculated water is caused to flow through a bed of sludge in the form of such dense and granular floc and denitrifying bacteria. The bed is subject to turbulent but intermittent agitation. A denitrified effluent is recovered. This denitrified effluent is caused to flow through a biological filter or preferably through a fluidized bed containing nitrifying bacteria and into which oxygen or air is injected. A clarified effluent is obtained, some of which is recycled as the diluting water.