The invention relates to a process for filtration of fluids, especially of aqueous media, by means of a backflush filter apparatus consisting of a cylindrical housing, a cylindrical and perforated support body installed coaxially therein, a filter material, a support fabric, and a mobile backflush device present therein, said process enabling improved removal of fine and ultrafine particles, and of particles with greasy or compressible consistency, and allowing higher solid concentrations. The process according to the invention has the steps below. a) Formation of a filtercake in the perforation of the support body; b) deposition of the relatively fine particles or of the particles with greasy or compressible consistency on or in the filtercake; c) backflushing after attainment of the predefined filter loading or of the maximum permissible pressure differential, or when the filtrate volume flow goes below a minimum. A further aspect of the invention is a filter apparatus for performance of the process, characterized in that the filter material consists of a filter fabric with an air permeability of 700-1300 l/m2s at pressure differential 200 Pa.