To make the apparatus compact, make steam with a high degree of dryness obtainable, and enable easily controlling demineralized water by controlling the quantity of feedwater on the basis of the temperature on the downstream side of the heating tube through which steam is led out from the downstream side.

In a controlling apparatus, the temperature of a superheater tube 4 at a coiled part 5 on the downstream side is monitored by a temperature detector 21 and according to the variation of the detected temperature T, it is detected at what degree the superheat stands at the coiled part 5; on the basis of the difference between this degree at which the superheat stands and a set temperature the flow rate in a water-feeding means 7 is continuously controlled in such a manner as to have the temperature T detected by the temperature detector 21 at a specified point or within a specified temperature range. By controlling a power-regulating means 22 according to variation of the detected temperature T the electric power supplied to an induction coil 2 of the superheater tube 4 is regulated and furthermore by on and off control the temperature at the coiled part 5 is so controlled as to be brought to a prescribed set point or within a set temperature range. Therefore it is desirable to attach the temperature detector 21 at a spot liable to be overheated in the superheater tube 4.