Abstract: A description is given of a process and an apparatus for the removal of volatile constituents, in particular solvents, monomers or oligomers, from polymer compositions or polymer solutions by evaporating the volatile components from the preheated polymer compositions in the form off free-falling films, strands (4) or foaming liquids in an evaporator system (1). In the process, following partial or complete degassing of the volatile components in the degassing space (9) of the evaporator system (1), the degassed polymer composition (4) is received at the lower end of the evaporator system (1) directly by a discharge delivery device (5) and is discharged, thereby avoiding contact of the polymer with the inside wall of the evaporator system (1).