The present invention relates to a process for concurrently removing CO2 and SO2 from flue gas produced by a combustion process, comprising: (a) performing a combustion process by combusting a fuel and air in a combustion apparatus, thereby creating an exhaust stream comprising CO2 and SO2; (b) compressing the exhaust stream in a first compression step, thereby producing a first compressed gas stream; (c) providing a first membrane having a feed side and a permeate side, and being selectively permeable to CO2 and SO2 over nitrogen and to CO2 and SO2 over oxygen; (d) passing at least a portion of the first compressed gas stream across the feed side; (e) withdrawing from the feed side a CO2- and SO2-depleted residue stream; (f) withdrawing from the permeate side at a lower pressure than the first compressed gas stream, a first permeate stream enriched in CO2 and SO2; (g) passing the first permeate stream to a separation process that produces a stream enriched in CO2 and a stream enriched in SO2.