In a reactor for the gasification of solid and liquid fuels in the entrained flow at temperatures between 1200 and 1900° C. and pressures between ambient pressure and 10 MPa with an oxidizing agent containing free oxygen, the cooling screen is connected in a gas-tight manner to the pressure shell via a bellows compensator to accommodate linear deformation. Continuous sweeping by gas of the annular gap between pressure shell and cooling screen is unnecessary and backflow by producer gas is prevented.