A process for removing carbon dioxide from a fluid comprises the steps of: (a) treating the fluid by bringing it into countercurrent contact with a liquid absorbent in a first absorption zone and thereafter in a second absorption zone to absorb at least part of the carbon dioxide contained in the fluid into the absorbent; (b) depressurizing the loaded absorbent to release a first stream of carbon dioxide and yield a partially regenerated absorbent; (c) recycling a first stream of the partially regenerated absorbent into the first absorption zone; (d) heating a second stream of the partially regenerated absorbent to release a second stream of carbon dioxide and yield a regenerated absorbent; (e) recycling the regenerated absorbent into the second absorption zone; (f) condensing water vapor entrained in the second stream of carbon dioxide by cooling the second stream of carbon dioxide and transferring at least part of the heat recovered to the partially regenerated absorbent by indirect heat exchange. The invention provides a two-stage carbon dioxide recovery process wherein the overall energy required for carbon dioxide recovery is reduced and/or wherein at least part of the carbon dioxide is recovered at a pressure higher than atmospheric pressure so as to reduce the energy required for compression of the carbon dioxide, e.g., for sequestration. Also disclosed is a plant for removing carbon dioxide from a fluid.