The invention relates to the fields of semiconductor, LED and photovoltaic solar energy production and the like, in particular to a ultrahigh-purity oxygen gas and nitrogen gas purification method. The method has the main technical scheme that the method comprises a catalytic oxidation work procedure, a drying deoxidation work procedure and a regeneration work procedure, wherein the catalytic oxidation work procedure comprises the following steps that raw material gas enters a heat exchanger from a raw material gas inlet to perform heat exchange and then enters a catalytic dealkylation device; impurities of H2, CO, CH4 and TCH in the raw material gas are converted into H2O and CO2 in the catalytic dealkylation device; the raw material gas enters a water cooler for temperature reduction again through the heat exchanger; a heating system and oxidization catalysts are arranged in the catalytic dealkylation device. The impurities of H2O, CO, CO2, CH4, TCH and the like in oxygen gas or nitrogen gas can be deeply removed; the oxygen gas impurity in the nitrogen gas can be removed; the problems that the gas impurities influence the device production in the electronic industry, and the electronic element quality reduction is caused are solved.