Abstract: An incoming stream of gas mixture typically comprising methane and up to 12% by volume of carbon dioxide is subjected to rectification in a first column to form a carbon dioxide depleted fraction that is withdrawn as product from the top of the column and a carbon dioxide-enriched fraction which is withdrawn from the bottom of the column is warmed in a heat exchanger and is introduced into a second rectification column operating at a higher pressure than the first column. A stream in which carbon dioxide predominates is withdrawn from the bottom of the higher pressure column while a stream 34 containing a lower proportion of carbon dioxide than said enriched fraction is withdrawn from the top of the higher pressure column is throttled through a valve and is united with the incoming stream of gas mixture upstream of or in the lower pressure column.