NOVELTY - A hydrogen generating system comprises a first back-pressure setting mechanism (34a), which sets a first back pressure for operating back-pressure valve mechanism (32) and discharging hydrogen to the outside of hydrogen supply passage; and a second back-pressure setting mechanism (34b), which sets a second back pressure at a pressure higher than that of the first back pressure for operating the back-pressure valve mechanism and extracting the high-pressure hydrogen into the hydrogen supply passage.    USE - A hydrogen generating system.    ADVANTAGE - The system eliminates impurity oxygen from hydrogen generated by water electrolysis, and is capable of obtaining high-purity hydrogen both easily and reliably, which is supplied to the hydrogen supply passage.    DETAILED DESCRIPTION - A hydrogen generating system comprises a first back-pressure setting mechanism (34a), which sets a first back pressure for operating back-pressure valve mechanism (32) and discharging hydrogen to the outside of hydrogen supply passage; and a second back-pressure setting mechanism (34b), which sets a second back pressure at a pressure higher than that of the first back pressure for operating the back-pressure valve mechanism and extracting the high-pressure hydrogen into the hydrogen supply passage. The system is equipped with a water electrolysis unit (14) for performing electrolysis on water, such that when hydrogen generated by the water electrolysis unit is developed into high-pressure hydrogen at or above a predetermined pressure, the high-pressure hydrogen is extracted into the hydrogen supply passage via a back-pressure valve mechanism. The system further comprises an oxygen concentration meter (40) for detecting oxygen concentration in the hydrogen generated by the water electrolysis unit. An INDEPENDENT CLAIM is included for a method for operating the hydrogen generating system.    DESCRIPTION OF DRAWING(S) - The drawing shows an outline structural schematic view of a hydrogen generating system.    Water electrolysis unit (14)    Back-pressure valve mechanism (32)    First back-pressure setting mechanism (34a)    Second back-pressure setting mechanism (34b)    Oxygen concentration meter (40)