Plural absorption stages for hydrogen purification

For the production of hydrogen, hydrocarbons are subjected to a partial oxidation, the resulting gaseous fraction is fed to a CO shift conversion and the acid gases are removed by absorption. To obtain a H2 product with a purity of at least 99% by volume without reduction in yield, sulfur compounds are removed in a first absorption stage with an organic, physical solvent; the resultant desulfurized gas is subjected to a selective catalytic oxidation with oxygen to selectively convert CO to CO2, and resultant desulfurized CO-depleted gas is treated in a second absorption stage with preferably the same scrubbing agent as first absorption stage to remove CO2.