Abstract: A layer of small-sized particles of an organic ion exchange resin is applied to a support matrix, permeable to liquid, of a filter element (7) which is arranged in a chamber (5) in an ion-exchange filter (1) for filtering of liquids containing radioactive constituents. The filter and a mixer (11), consisting of a tube with a number of stationary mixing elements arranged one after the other in the longitudinal direction of the tube, are arranged in a circulation system (10) for water. The mixing elements successively divide up a material flow, supplied at the inlet end of the mixer, into a number of sub-flows containing different parts of the original material flow and the sub-flows are reunited, before they reach the outlet end of the tube. Suspended ion-exchange resin (13a, 16a) is supplied to the inlet end (11a) of the mixer for the circulating water while the water is being circulated in the circulation system.