Abstract: The invention relates to a separating device, more particularly for hemodialysis, comprising a housing accommodating at least one bundle of a large number of tubular, selectively permeable membranes connected in parallel whose transverse dimensions are very small relative to their longitudinal dimensions. The ends of the membranes rest on supporting members in the housing. The membranes may be the walls of hollow fibers which divide the internal part of the separating device into a first medium space provided by the inside of the membranes and a second medium space inside the housing but outside the membranes. The medium spaces are each provided with an inlet and an outlet for respectively the supply and the discharge of a first and a second medium, which media can enter into exchange through the walls of the membranes.