The invention relates to a fluidized-bed furnace comprising a combustion fluidized bed (6a), to which the fuels to be fired are fed, and comprising a heat-exchanger fluidized bed (6b), to which immersion heating surfaces (17) are assigned. A heat discharge from the combustion fluidized bed (6a) is produced by bed material being passed from the combustion fluidized bed (6a) to the heat-exchanger fluidized bed (6b). A return unit is provided, by means of which a continuous, controllable material circulation is set up between the combustion fluidized bed and the heat-exchanger fluidized bed. The return unit may be formed as a tube structure or a greatly expanded fluidized bed. Multiple systems can be combined to form larger units.