TECHNOLOGY FOCUS - CHEMICAL ENGINEERING - Preferred System: In the system, at least one of the stages (31, 32) has membranes selective to CO2 and at least one other of the stages (31, 32) has membranes permeable to H2 and other fuel gases contained in the anodic exhaust, such as carbon monoxide (CO), methane (CH4), etc., and CO2, but tendentially impervious to water vapor; or else membranes permeable to water vapor but tendentially impervious to the other gases present in the anodic exhaust. The separation device (8) comprises high-temperature membranes, operating at temperatures of approximately 450 degrees C to 650 degrees C, and/or medium-temperature membranes, operating at temperatures of approximately 250 degrees C to 450 degrees C. The membranes of the separation stages (31, 32) are configured in such a way that the separation device (8) as a whole produces at least, as distinct flows: a flow (F1) with high CO2 content, which contains the major portion of the CO2 initially present in the anodic exhaust; a flow (F2) containing the majority of the H2 present in the anodic exhaust; and a flow (F3) with high water-vapor content. It comprises a primary-fuel-conversion unit (9), which is connected to a cathodic compartment (7) of the, fuel cell (5) via a cathodic-recirculation line (24) where the separation device (8) is connected to a burner (10) of the conversion unit (9) in such a way as to supply the burner (10) with the flow (F2) produced by the separation device (8) containing the majority of the H2 present in the anodic exhaust. The separation device (8) is connected to a turbine (13) in such a way as to supply the turbine (13) with the flow (F3) with high water-vapor content produced by the separation device (8). The separation device (8) is a two-stage separation device, having two membrane separation stages (31, 32) operating in series with respect to the retentate or with respect to the permeate. Preferred Method: In separating CO2 and recovering fuel from anodic exhaust gas of molten-carbonate fuel cells, the first separation step is conducted by supplying the first stage (31) with anodic exhaust coming from the anodic compartment (6); and the separation steps produce respective permeates and retentates and are conducted in series with respect to the retentates or with respect to the permeates. The separation steps produce at least, as distinct flows: a flow (F1) with high CO2 content, which contains the major portion of the CO2 initially present in the anodic exhaust; a flow (F2) containing the majority of the H2 present in the anodic exhaust; and a flow (F3) with high water-vapor content. It comprises a step of supply of the flow (F2) containing the majority of the H2 present in the anodic exhaust to a primary-fuel-conversion unit (9), and a step of conversion or reforming of primary fuel into gaseous fuel suitable for supply of the anodic compartment (6) with the aid of the flow (F2) containing the majority of the H2 present in the anodic exhaust. In the conversion step the flow (F2) containing the majority of the H2 present in the anodic exhaust supplies heat for sustaining a reaction of conversion or reforming of the primary fuel. It comprises a step of supply of the flow (F3) with high water vapor content to a turbine (13). The membranes are high-temperature membranes, operating at temperatures of approximately 450 degrees C to 650 degrees C and/or medium-temperature membranes, operating at temperatures of approximately 250 degrees C to 450 degrees C.