The present invention provides a process for recovering hydrogen and carbon dioxide from a process stream (1) of a process unit (0) wherein the process stream (1) contains at least carbon dioxide, hydrogen and methane. In the process, the process stream (1) is optionally compressing in a first compressor (2) before being cooled in a heat exchanger (3) to a temperature equal to or less than −10° C. Next, the cooled process stream (1) is separated and purified in a carbon dioxide separation unit (4) to produce a carbon dioxide rich liquid stream (6) and a carbon dioxide lean non-condensable stream (5) with the carbon dioxide rich liquid stream (6) being withdrawn as a carbon dioxide product for further use. The carbon dioxide lean non-condensable stream (5) is then withdrawn from the carbon dioxide separation unit (4) and passed through a hydrogen selective membrane separation unit (7) to form a hydrogen rich permeate stream (8) with the remaining components in the carbon dioxide lean non-condensable stream (5) forming a hydrogen lean residue stream (9). The hydrogen lean residue stream (9) is passed through a carbon dioxide selective membrane separation unit (10) to form a carbon dioxide enriched permeate stream (11) with the remaining components in the hydrogen lean residue stream (9) forming a carbon dioxide depleted residue stream (12). The hydrogen rich permeate stream (8) is optionally compressed in a second compressor (13) and recycled for use as a supplemental feed stream in the process unit (0) or in other processes. The carbon dioxide enriched permeate stream (11) is recycled to the process stream (1) prior to the compressor (2) or within the compressor (2) between stages of compression, or to the carbon dioxide separation unit (4) while the carbon dioxide depleted residue stream (12) is withdrawn for further use. The present invention further relates to the use of this process within a hydrogen generation plant to increase recovery of hydrogen and capture equal to or greater than 90% of the carbon dioxide in the syngas stream.