A continuous process for synthesizing a polymer with separation of a gaseous substance in an apparatus comprising - a reaction space having an upper section, a middle section and a lower section, - an inlet orifice disposed in the middle section, - a first outlet orifice disposed in the lower section, - a second outlet orifice disposed in the upper section, - a first return orifice disposed in the lower section, - a second return orifice disposed beneath the upper section, where the first return orifice and the second return orifice are connected to one another by a return line in which there is disposed a pump set up to transport a liquid from the first return orifice to the second return orifice, - a distributing device which delimits the middle section from the upper section, and - a removal device disposed so as to be movable along the upper section, where the removal device has a removal head disposed on the inner wall at the top of the middle section and where the removal head makes contact with the inner wall at the top of the middle section with deformation of the edges of the removal head, where - the inlet orifice is connected by means of an inlet line to a wall of the upper section, the removal head having an orifice through which the inlet line is conducted, having the following process steps: a) feeding a prepolymer melt into a middle section of a reaction space through an inlet orifice, b) transporting a portion of the prepolymer melt from a lower section of the reaction space disposed below the middle section into an upper section of the reaction space above the middle section and distributing the prepolymer melt over the inner wall of the middle section by means of a distributing device, c) polymerizing the prepolymer melt to give a polymer melt, d) removing the polymer melt from the reaction space through a first outlet orifice of the reaction space, and e) removing a gaseous substance from the reaction space through a second outlet orifice in the upper section, wherein deposits on at least one inner wall of the upper section are removed by a removal device. - a reaction space having an upper section, a middle section and a lower section, - an inlet orifice disposed in the middle section, - a first outlet orifice disposed in the lower section, - a second outlet orifice disposed in the upper section, - a first return orifice disposed in the lower section, - a second return orifice disposed beneath the upper section, where the first return orifice and the second return orifice are connected to one another by a return line in which there is disposed a pump set up to transport a liquid from the first return orifice to the second return orifice, - a distributing device which delimits the middle section from the upper section, and - a removal device disposed so as to be movable along the upper section, where the removal device has a removal head disposed on the inner wall at the top of the middle section and where the removal head makes contact with the inner wall at the top of the middle section with deformation of the edges of the removal head, where - the inlet orifice is connected by means of an inlet line to a wall of the upper section, the removal head having an orifice through which the inlet line is conducted, a) feeding a prepolymer melt into a middle section of a reaction space through an inlet orifice, b) transporting a portion of the prepolymer melt from a lower section of the reaction space disposed below the middle section into an upper section of the reaction space above the middle section and distributing the prepolymer melt over the inner wall of the middle section by means of a distributing device, c) polymerizing the prepolymer melt to give a polymer melt, d) removing the polymer melt from the reaction space through a first outlet orifice of the reaction space, and e) removing a gaseous substance from the reaction space through a second outlet orifice in the upper section,