In a reactor for gasification of entrained solid and liquid fuels at temperatures between 1,200 and 1,900° C. and at pressures between ambient pressure and 10 MPa using an oxidizing agent containing free oxygen, the cooling screen is connected to the pressure shell in a gastight manner via a sliding seal in order to allow length changes. Continuous gas purging of the annular gap between pressure shell and cooling screen is unnecessary and gasification gas is prevented from flowing behind.