A method of and an apparatus for the filtering of a fluid in which a filter-aid agent of a particulate or fibrous character is floated onto and deposited upon a support fabric in a fluid. The medium to be filtered is then passed through the filter layer formed by this filter aid. The fabric divides the filter chamber into two compartments both of which are flushed with washing liquid which is discharged from the upstream compartment after back-washing through the fabric. During the filtration, a loss of the purified filtrate and a mixture with nonfiltered medium is precluded in that both compartments, after the filtering and cleaning phases, are completely discharged of fluid. The backwashing of the fabric is effected with another fluid.