A method is disclosed for the separation of ethane and heavier hydrocarbons or propane and heavier hydrocarbons from natural gas to provide a methane-rich natural gas stream and less volatile natural gas liquids (NGLs). This method provides for the use of a regenerable adsorbent media comprising a porous cross-linked polymeric adsorbent, a pyrolized macroporous polymer, or mixtures thereof, which is regenerated by a pressure swing adsorption (PSA) process, temperature swing adsorption (TSA) process, or combination of the two. Said regeneration step may be operated as a batch process, a semi-continuous process, or preferably as a continuous process.