The invention relates to refining and separating a krypton-xenon concentrate. The inventive method consists in dividing said krypton-xenon concentrate into krypton and xenon fractions in a pre-separation column, in addition removing semi-volatile impurities from each fraction, obtaining production krypton and xenon from said refined fractions in krypton and xenon columns and in addition extracting krypton from stripping gas of the krypton column by the rectification thereof. Reflux is formed in condensers-evaporators of the rectification columns in such a way that the formation of a solid phase is excluded. The operation of the rectification columns is initiated by supplying krypton to a contacting space. The inventive device for carrying out said method is also disclosed. Said invention makes it possible to increase the economical efficiency of the production of pure krypton and xenon by means of the maximum extraction thereof from an initial mixture.