A method of stabilizing pressure and flow conditions in a screening apparatus for treating a pulp is described, the pulp being supplied continuously to the screening apparatus through an inlet and passed through a pulp space along a screen of a screen body and discharged continuously through an outlet, said screen body being moved axially with a forward-going movement during an extraction phase and a backward-going movement during a backflushing phase. The flowrate of the pulp through, and the pressure conditions in, the treating zone of the screening apparatus are controlled by altering the volume at the inlet end and outlet end of the screening apparatus during the movement of the screen body. A screening apparatus for carrying out the method is also described, which comprises a cylinder housing with a piston movable to and fro therein by means of a drive device, said piston defining a first chamber filled with liquid and a second chamber filled with pulp, said pulp chamber being in direct communication with the pulp inlet. Furthermore, a connection channel filled substantially with liquid is disposed between the liquid chamber and an outlet zone of the pulp space located at the outlet for treated pulp.
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