In a process and apparatus used to produce krypton and/or xenon by low-temperature fractionation of air, compresses and clean charge air (1) is introduced into a rectification system for nitrogen-oxygen separation. The rectification system includes at least a high-pressure column (2) and a low-pressure column (3). A krypton- and xenon-containing fraction (13, 14, 15, 16) is removed from the high-pressure column (2) and introduced into the evaporation space of a condenser-evaporator (17), where it is partially evaporated. A purge liquid (26) is extracted from the evaporation space of the condenser-evaporator (17) and fed to a krypton-xenon enrichment column (24). A krypton-xenon concentrate (30) is removed from the krypton-xenon enrichment column (24). A liquid from the lower region of the krypton-xenon enrichment column (24) is introduced into a second condenser-evaporator (27), which is separate from the first condenser-evaporator (17).