Disclosed herein are 2-stage membrane separation methods for capturing CO.sub.2 from a feed gas. The methods can employ two selectively permeable membranes, which may be the same or different. The selectively permeable membrane can have a carbon dioxide permeance of from 500 to 3000 GPU at 57° C. and 1 atm feed pressure and a carbon dioxide:nitrogen selectivity of from 10 to 1000 at 57° C. and 1 atm feed pressure. High pressure ratios across the membranes can be achieved by compressing the feed gas to a high pressure, by using vacuum pumps to create a lowered pressure on the permeate side of the membrane, by using a sweep stream, or a combination thereof. When a sweep stream is used, the sweep stream may include a portion of the retentate gas stream obtained from the retentate side of one or more of the membranes used.

Disclosed herein are 2-stage membrane separation methods for capturing CO.sub.2 from a feed gas. The methods can employ two selectively permeable membranes, which may be the same or different. The selectively permeable membrane can have a carbon dioxide permeance of from 500 to 3000 GPU at 57? C. and 1 atm feed pressure and a carbon dioxide:nitrogen selectivity of from 10 to 1000 at 57? C. and 1 atm feed pressure. High pressure ratios across the membranes can be achieved by compressing the feed gas to a high pressure, by using vacuum pumps to create a lowered pressure on the permeate side of the membrane, by using a sweep stream, or a combination thereof. When a sweep stream is used, the sweep stream may include a portion of the retentate gas stream obtained from the retentate side of one or more of the membranes used.