The present invention relates to a pressure-temperature swing adsorption process wherein gaseous components that have been adsorbed can be recovered from the adsorbent bed at elevated pressures. In particular, the present invention relates to a pressure-temperature swing adsorption process for the separation of C2+ hydrocarbons (hydrocarbons with at least 2 carbon atoms) from natural gas streams to obtain a high purity methane product stream. In more preferred embodiments of the present processes, the processes may be used to obtain multiple, high purity hydrocarbon product streams from natural gas stream feeds resulting in a chromatographic-like fractionation with recovery of high purity individual gaseous component streams.