With a method for the generation of synthesis gas by means of gasification of solid or liquid carbonaceous fuels with an oxidation agent containing oxygen, in a reactor, wherein the synthesis gas is passed out of the reactor overhead, and the mineral ash/slag droplets that occur during the reaction are passed out of the reactor downward, in the direction of gravity, it is supposed to be made possible to use a flue-tube boiler, which is clearly less expensive, for heat removal in place of radiant boilers. This is achieved in that the synthesis gas is passed over a hot-gas filter (2), without being cooled, and subsequently passed through a flue-tube boiler (3), for cooling, wherein ash/slag particles precipitated on the hot-gas filter (2) are passed back into the gasification reactor (1), in the direction of gravity.