Abstract: The glycerol water (sweet water) accumulating in the high-pressure hydrolysis of natural fats and oils with steam into fatty acid and glycerol is continuously purified. Fats larger than 100 .mu.m in diameter are separated from the aqueous phase in a plate-type phase separator and are returned to the high-pressure hydrolysis process. The aqueous phase thus prepurified is passed through a cross-flow filtration membrane, more particularly a microfiltration membrane, and the concentrate is returned to the entrance of the plate-phase separator. Large product streams of glycerol water can be purified continuously, effectively and particularly economically despite frequent changes of provenance.