A process for controlling carbon dioxide exhaust from a combustion process, comprising: (a) compressing an oxygen-containing stream in a first compression step, thereby producing a first compressed gas stream; (b) routing at least a portion of the first compressed gas stream to a gas separation apparatus adapted to selectively remove carbon dioxide, thereby producing a carbon dioxide-enriched stream and a carbon dioxide-depleted stream; (c) compressing the carbon dioxide-depleted stream in a second compression step, thereby producing a second compressed gas stream; (d) combusting at least a portion of the second compressed gas stream with a gaseous fuel in a combustion apparatus, thereby producing a combusted gas stream; (e) routing the combusted gas stream as part of a working gas stream to a gas turbine apparatus mechanically coupled to an electricity generator, and operating the gas turbine apparatus, thereby generating electric power and producing a turbine exhaust stream; (f) passing at least a portion of the turbine exhaust stream to a membrane separation step, wherein the membrane separation step comprises: (i) providing a membrane having a feed side and a permeate side, and being selectively permeable to carbon dioxide over nitrogen and to carbon dioxide over oxygen, (ii) passing the first portion of the turbine exhaust stream across the feed side, (iii) passing air, oxygen-enriched air, or oxygen as a sweep stream across the permeate side, (iv) withdrawing from the feed side a residue stream that is depleted in carbon dioxide compared to the turbine exhaust stream, and (v) withdrawing from the permeate side a permeate stream comprising oxygen and carbon dioxide; and (g) passing the permeate stream to step (a) as at least a portion of the oxygen-containing gas. (a) compressing an oxygen-containing stream in a first compression step, thereby producing a first compressed gas stream; (b) routing at least a portion of the first compressed gas stream to a gas separation apparatus adapted to selectively remove carbon dioxide, thereby producing a carbon dioxide-enriched stream and a carbon dioxide-depleted stream; (c) compressing the carbon dioxide-depleted stream in a second compression step, thereby producing a second compressed gas stream; (d) combusting at least a portion of the second compressed gas stream with a gaseous fuel in a combustion apparatus, thereby producing a combusted gas stream; (e) routing the combusted gas stream as part of a working gas stream to a gas turbine apparatus mechanically coupled to an electricity generator, and operating the gas turbine apparatus, thereby generating electric power and producing a turbine exhaust stream; (f) passing at least a portion of the turbine exhaust stream to a membrane separation step, wherein the membrane separation step comprises: (i) providing a membrane having a feed side and a permeate side, and being selectively permeable to carbon dioxide over nitrogen and to carbon dioxide over oxygen, (ii) passing the first portion of the turbine exhaust stream across the feed side, (iii) passing air, oxygen-enriched air, or oxygen as a sweep stream across the permeate side, (iv) withdrawing from the feed side a residue stream that is depleted in carbon dioxide compared to the turbine exhaust stream, and (v) withdrawing from the permeate side a permeate stream comprising oxygen and carbon dioxide; and (i) providing a membrane having a feed side and a permeate side, and being selectively permeable to carbon dioxide over nitrogen and to carbon dioxide over oxygen, (ii) passing the first portion of the turbine exhaust stream across the feed side, (iii) passing air, oxygen-enriched air, or oxygen as a sweep stream across the permeate side, (iv) withdrawing from the feed side a residue stream that is depleted in carbon dioxide compared to the turbine exhaust stream, and (v) withdrawing from the permeate side a permeate stream comprising oxygen and carbon dioxide; and (g) passing the permeate stream to step (a) as at least a portion of the oxygen-containing gas.