Abstract: A process for removing carbon dioxide regeneratively from a hot gas stream, containing flue gases or fuel gases, wherein the gas stream is successively: a) used for heating (1) and/or desorbing (2) a solid absorbent loaded with carbon dioxide; b) optionally used for generating energy (12); c) passed through an absorber (3) in which carbon dioxide from the gas stream is absorbed on the absorbent, and: d) is discharged (11); and wherein: e) the absorbent from step c) is desorbed in ta desorber (2) at least partially and optionally under elevated pressure and is then returned to step c). A system for carrying out the process is also described. The process and the system are suitable for removing carbon dioxide from combustion gases and for shifting (coal) gasification gases toward hydrogen.