NOVELTY - In a fixed bed reactor for biological purification of fluids comprising a vertical reactor vessel (10) in which the fluid flows upwards through the fixed bed, the reactor vessel is provided with: (a) a rotably mounted, fluid-permeable retaining element (12) and/or (b) a fluid entry zone (12), formed correspondingly to the reactor vessel, in which fluid to be purified is mixed with the fluid present in the fixed bed reactor.    USE - Especially for aerobic and anerobic purification of waste water (claimed). The charging arrangement is for supplement the fixed bed with fresh loose bodies to compensate for loose bodies which have lost their coating of purifying microorganisms by abrasion during operation, so that high purification performance is retained.    ADVANTAGE - The arrangement creates the required plug flow, even during prolonged operation. The whole fixed bed is moved in a homgeneous plug flow, without intensive mixing of the loose bodies forming the fixed bed. Colonization of the bodies by the microorganisms is thus not disrupted, which promotes complete degradation of organic intermediate metabolites, increases product yield and ensures effective and intensive purification.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are claimed for corresponding purification methods, in which:    (a) the fluid to be purified is supplied to an entry zone, in which its mixed and homogenized with the fluid already present before being flowing into the fixed bed reactor and/or    (b) the fixed bed is moved transverse to the flow direction.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic sectioned side view of the reactor.    Reactor vessel (10)    Retaining element (12)    Lid of retaining element (13)    Partition (14)    Base of retaining element (15)    Pipe (18)    Shaft (19)    Stirred tank (20)    Stirrer (22)    Sludge reservoir (24)    Sludge outlet (26)    Fluid inlet (28)    Gas entry line (30)    Lid of reactor (31)    Gas outlet (32)    Liquid outlet (34)    Recycling pump (36)