Abstract: A system for the conversion of liquid phases of non-metallic substances into solid phases, especially polymerizable or crystallizable substances, provides a reaction chamber in the form of an upstanding substantially tubular-shaped hollow body, at the upper end of which there is introduced the liquid phase and at the lower end of which there is continuously withdrawn the solid phase. The reaction chamber is enclosed at least at its upper region containing the liquid phase by a jacket of polygonal cross-section, wherein the wall sections of the chamber which in cross-section is polygonal are formed in each case by a run of an endless band which bears against the associated jacket section, each such band moving continuously downwardly by means of the aforesaid run and being substantially synchronously driven with the remaining bands.