The invention relates to cryogenic engineering, in particular to purifying krypton-xenon mixture and is usable in the chemical and oil-and-gas industries. The inventive method comprises purifying and separating the mixture in rectification columns, wherein coolant is removed and returned to a cooling cycle, additionally removing radionuclides from krypton and xenon fractions and from krypton and xenon production flows by means of filtration and/or adsorption and/or rectification and/or absorption and/or chemical and/or physicochemical methods in apparatuses for additional removing radionuclides. Balloons for reception of the separated products are certified with respect to radionuclides content and/or activity prior to and after the filling thereof. An installation for carrying out the method is also disclosed, allowing to additionally remove radionuclides from the separated products in such a way that the products can be used, for example, for medical purposes and to increase the cost efficiency of purification and separation processes.