The invention relates to a continuous steam generator provided with an evaporator through flow heating surface which is disposed in a heating gas channel which can be cross flown in an approximately vertical manner in a heating gas device, said evaporator through flow heating surface comprising a plurality of parallel connected steam generating pipes enabling a flow medium to flow through, and an overheating heating surface which is arranged downstream from the evaporator through flow heating surface comprising a plurality of parallel connected overheating pipes enabling the evaporated flow medium to flow through, also enabling production and operational costs to be reduced and enabling the temperature of the steam on the outlet of the overheating heating surface to be controlled in a comparatively simple and flexible manner. The steam end-point of the flow medium is displaced to the overheating pipe, if required. The continuous heating surfaces and the overheating heating surfaces are combined to form one functional unit such that the overheating heating surface can be used as a steam heating surface in a continuous steam generator which is particularly suitable for carrying out said method.