An apparatus for stabilizing liquid includes first and second filters, intermediate storage that stores a regenerable stabilizing agent, an inlet line supplying unstabilized liquid and connected to both filters and to the intermediate storage, and a switchable interconnection configured for, immediately after regeneration and cleaning of the first or second filter, selectively causing the one of the first filter unit and the second filter unit to be upstream of an other of the first filter unit and the second filter unit. The first filter unit and the second filter unit are configured to run in different operational phases that are offset in time from one another.