Xenon and/or krypton is separated from a liquid oxygen stream comprising oxygen and xenon and/or krypton in a process comprising providing at least a portion of the liquid oxygen stream as a reflux liquid to the top of a rare gas recovery column operated at a pressure of between 5 to 25 bara, vaporizing a reboiler liquid in the reboiling zone in the bottom of the rare gas recovery column to produce a mixture of a rising vapor and a xenon and/or krypton-enriched liquid stream; and contacting the rising vapor with the reflux liquid in at least one distillation zone of the column to effect stripping xenon and/or krypton from the rising vapor to the reflux liquid. The process provides a recovery of xenon of greater than 90% and a krypton recovery of 15% to 90%.