Apparatus for the polymerization of olefins, in particular ethylene, comprising a gas-phase fluidized-bed reactor (1), a product offtake line (15) for taking polymer particles either continuously or discontinuously from the reactor (1), which line (15) is connected to a depressurization vessel (2) for separating polymer particles and gas, a recycle gas filter (3) for freeing the gas of entrained fine particles connected to the depressurization vessel (2), a compressor which compresses the gas which has been freed of fine particles and recirculates it into the reactor (1), with the recycle gas filter (3) having an inlet chamber (4) provided with a gas inlet (6), an outlet chamber (5) provided with a gas outlet (7), an essentially vertical sheet-like filter medium (9) for retaining the fine particles which separates the inlet chamber (4) from the outlet chamber (5) and a particle outlet (8). The inlet chamber (4) has a dividing wall (10) which is arranged essentially parallel to the filter medium (9) and separates the inlet chamber (4) into an inflow region (4a), which is connected to the gas inlet (6), and a filter region (4b) in which the filter medium is located and has an upper opening and a lower opening which are dimensioned so that from 60 to 90% of the volume flow flows through the upper opening so that flow along the filter medium (9) from the top downward results.