A process of supplying moisture at low flow rates which permits high precision control of the flow of moisture to a semiconductor manufacturing line from an apparatus for the generation of moisture, characterized in that the flow of hydrogen to a moisture-generating reactor is controlled by means of a flow controller in such a way that an amount of hydrogen as fed is gradually increased from the start and reaches a specific set level such that when a specific time has passed, a predetermined rate of moisture begins to be produced and supplied to the semiconductor manufacturing line. The moisture is generated in the apparatus for generation of moisture in which hydrogen and oxygen are (a) fed into a reactor provided with a coat of platinum on the wall in the interior space, (b) enhanced in reactivity by the platinum catalytic action, and (c) caused to instantaneously react with each other at a temperature lower than the ignition point to produce moisture without undergoing combustion at a high temperature.