Abstract: A method of and apparatus for separating krypton from radioactive waste gases which become free during the chemical dissolution of burnt-off fuel particles and contain krypton and xenon. Simultaneously with the core fuel particles conveyed to the chemical dissolution, such quantity of chemically inactive carrier gas intermixable with the waste gases is added to the substances bringing about the chemical dissolution that after purification of the waste gas mixture from gas components such as oxygen, carbon dioxide, nitrous oxide, hydrocarbons and water steam and after subsequent cooling of the waste gas mixture to the boiling temperature of the liquid nitrogen, the quantity of xenon contained in the waste gas mixture is quantitatively precipitated in solid form. Thereupon the waste gas mixture is cooled by means of liquid nitrogen, while simultaneously increasing the pressure, to such an extent that krypton is precipitated.