A pressure swing adsorption process for the separation of nitrogen from a mixture of same with methane, utilizing two separate PSA stages, one containing a nitrogen selective adsorbent and the second containing a methane-selective adsorbent. In the process, the first PSA unit containing a nitrogen selective adsorbent forms a product methane stream and a waste stream rich in nitrogen which is passed to a second PSA unit containing a methane selective adsorbent which forms a product nitrogen stream and a waste stream rich in methane. The waste stream rich in methane can be treated to remove heavy hydrocarbons therefrom before the methane is recycled to feed.