In a process for the removal of protein and degradation products thereof from water, a filter material which has a large contact area is flushed by the water to be purified. In order to be able also to remove, in particular, the nitrate from the water, the filter material used is an inert carrier, such as plastics material, preferably foamed plastics material, expanded clay or the like, which contains bacteriophilic nutrients, such as lactose and/or dextrose and/or phthalic acid ester or the like, and which releases the latter slowly over a fairly long period of time, as a result of which the carrier forms an advantageous substrate for settlement by bacteria. An aerobic and an anaerobic reaction zone are set up in the filter material, so that both nitrification and denitrification can take place in the filter material.