A process and device for the gasification of liquid or fine-grain solid fuel materials in a reactor is described. Synthesis gas is generated in a first reaction chamber arranged in the upper part of the reactor; feedstock is fed to the upper part. Liquid slag precipitates on its lateral walls. The lower side has a hole with a slag drop-off edge; generated synthesis gas can be withdrawn in downward direction and the liquid slag can drop off the edge. A second chamber delimited by a water film is located under the opening. A third chamber adjacent to the bottom of the second is fed with water. A water bath is adjacent the bottom of the third chamber. The synthesis gas is withdrawn from the pressure vessel in an area at the side or below the third chamber, but located above the water bath.