A pressure swing adsorption process for the separation of impurities such as nitrogen and carbon dioxide and recovery of hydrocarbons from a natural gas stream utilizes two separate adsorption systems, the first (32) containing an adsorbent selective for nitrogen, carbon dioxide or both and the second (40) containing a hydrocarbon-selective adsorbent. In the process, the natural gas stream is passed through a first adsorbent to form a product stream (34) enriched with methane and to adsorb nitrogen and/or carbon dioxide and which further coadsorbs at least a portion of the hydrocarbons contained in the feed stream. The hydrocarbons are recovered by passing a low pressure waste stream (35) from the first pressure swing adsorption stage (32) which contains coadsorbed nitrogen and/or carbon dioxide and hydrocarbons and directing the waste stream to the second pressure swing adsorption stage (40) to adsorb the hydrocarbons and produce a product stream (42) enriched in nitrogen and/or carbon dioxide. The hydrocarbons are., recovered from the hydrocarbon-selective adsorbent by an intermediate pressure methane­containing stream (44) from the first pressure:swing adsorption stage which purges the adsorbent in the second stage which purges the.adsorbent in the second stage and forms a combined stream comprising methane and C.3 + hydrocarbons. The C3+ hydrocarbons can be separated from the methane such as by compression with flash separation or refrigeration.