An adsorption process for xenon recovery from a cryogenic liquid or gas stream is described wherein a bed of adsorbent is contacted with the aforementioned xenon containing liquid or gas stream and adsorbs the xenon selectively from this fluid stream. The adsorption bed is operated to at least near full breakthrough with xenon to enable a deep rejection of other stream components, prior to regeneration using the temperature swing method. Operating the adsorption bed to near full breakthrough with xenon, prior to regeneration, enables production of a high purity product from the adsorption bed and further enables oxygen to be used safely as a purge gas, even in cases where hydrocarbons are co-present in the feed stream.