This gas purifying process removes trace constituents from a mixed gas that includes a rare gas and nitrogen as main components, and at least one from among hydrogen, nitrogen and hydrogen reaction products, and water vapor as the trace constituent. This process sequentially carries out an adsorbing step for removing water vapor and nitrogen and hydrogen reaction products; a hydrogen oxidation step for converting the hydrogen into water vapor by means of a hydrogen oxidation catalytic reaction in the presence of oxygen; and a drying step for removing water vapor generated in the hydrogen oxidation step. When nitrogen oxides are included as a trace constituent, then a denitration step is carried out prior to the adsorbing step, to convert nitrogen oxides into nitrogen and water vapor by means of a catalytic denitration reaction in the presence of a reducing substance.