Separation of unwanted gases and/or finely divided particles from waste gas is achieved in transverse flow-through at least two vertical layers of granular adsorbent, esp. activated carbon or coke, which migrates downward. A feeder charges both layers from above, with both once-used and fresh adsorbent. The material is removed below. In a novel operation, adsorbent is so removed from one layer, in correspondence with the waste content of the adsorbent of the other layer, to form a waste material profile, slanting in one direction at given levels in its migration path. Also claimed is appts. to carry out the method.