A gas separation and power generation process, comprising the following steps: (a) compressing an oxygen-containing stream in a compression apparatus, thereby producing a compressed gas stream; (b) combusting a first portion of the compressed gas stream with a gaseous fuel in a combustion apparatus, thereby producing a combusted gas stream; (c) separating a second portion of the compressed gas stream in a gas separation apparatus adapted to selectively remove carbon dioxide, thereby producing a carbon-dioxide enriched stream and a carbon-dioxide-depleted stream, wherein the gas separation apparatus is a membrane separation apparatus; (d) routing the carbon-dioxide-depleted stream and the combusted gas stream as first and second working gas streams 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; (e) passing at least a first portion of the turbine exhaust stream to a sweep-based membrane separation step, wherein the sweep-based 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, (v) withdrawing from the permeate side a permeate stream comprising oxygen and carbon dioxide; and (f) passing the permeate stream to step (a) as at least a portion of the oxygen-containing gas; wherein the method further comprises routing a third portion of the compressed gas stream directly to the gas turbine inlet as a third working gas stream for step (d). (a) compressing an oxygen-containing stream in a compression apparatus, thereby producing a compressed gas stream; (b) combusting a first portion of the compressed gas stream with a gaseous fuel in a combustion apparatus, thereby producing a combusted gas stream; (c) separating a second portion of the compressed gas stream in a gas separation apparatus adapted to selectively remove carbon dioxide, thereby producing a carbon-dioxide enriched stream and a carbon-dioxide-depleted stream, wherein the gas separation apparatus is a membrane separation apparatus; (d) routing the carbon-dioxide-depleted stream and the combusted gas stream as first and second working gas streams 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; (e) passing at least a first portion of the turbine exhaust stream to a sweep-based membrane separation step, wherein the sweep-based 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, (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, (v) withdrawing from the permeate side a permeate stream comprising oxygen and carbon dioxide; and (f) passing the permeate stream to step (a) as at least a portion of the oxygen-containing gas;