A process is set forth for purifying and liquefying a feed gas mixture with respect to its less strongly adsorbed component of lower volatility which integrates temperature swing adsorption (TSA), pressure swing adsorption (PSA) and cryogenic distillation to optimize overall performance. The TSA portion of the process is used to remove the strongly adsorbed component from the feed; the PSA portion of the process is used to remove the moderately strongly adsorbed component from the feed; and the cryogenic distillation portion of the process is used to remove the less strongly adsorbed component of higher volatility from the feed while also providing for the liquefaction of the product. A key to the present invention is the use of the PSA and distillation waste streams in the regeneration of the TSA and PSA adsorbents. An important application of the present invention is the purification and liquefaction of a natural gas feed stream with respect to its methane/C.sub.2 hydrocarbon component.