Abstract: The invention provides a process for heterophase reactions in a liquid or supercritical dispersion medium, in which the starting materials are introduced into the reaction zone of a reactor provided with one or more enrichment zones and the reaction product or unreacted starting material or both starting material and reaction product are discharged via one enrichment zone in each case, wherein a) the reaction product together with the dispersion medium is discharged from the reactor via an enrichment zone, the reaction product is separated off and the dispersion medium is, if desired in countercurrent to the reaction product/dispersion medium mixture and via an enrichment zone, returned to the reaction zone, or b) unreacted starting material together with the dispersion medium is discharged, the starting material is separated from the dispersion medium and returned directly to the reaction zone and the dispersion medium is, if desired, in countercurrent to the reaction product/dispersion medium mixture and vi