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The problem of suspension filtration has been considered with allowance for the formation of a precipitate by sedimenting disperse particles in one dimensional formulation. The behavior of a suspension is described with a set of equations for the one dimensional inertialess motion of a two phase mixture, and the motion of a liquid through a porous precipitate layer has been described with a filtration equation based on the Darcy law. The particular (limit) cases of an equidense suspension (when the densities of both solid and liquid phases are equal) and an equilibrium suspension (when the sizes of particles are small enough to neglect their sedimentation) and the asymptotic case when the density of disperse particles is much greater than the density of a liquid phase have been studied. Some formulas for the characteristic times of disperse phase sedimentation and liquid filtration have been derived. The limit regimes of slow filtration and slow sed imentation are analyzed. In the general case, the problem has been solved in implicit form.