Abstract: This invention relates to a process and a reactor for conducting exothermal reactions, for instance combustion, between relatively heavy and relatively light phases in a circulating fluidized bed having vertical cooling surfaces for absorption of the reaction heat resulting from the reaction. The light phase is divided into a primary flow for maintaining a dense conventional part bed and a secondary flow for maintaining a less dense rapid part bed above the dense bed. Said rapid part bed is recycled outside the part beds to the dense part bed for producing the circulating bed. Solid phase is continuously supplied to and withdrawn from the circulating bed, and the secondary flow is supplied to the circulating bed mainly below the cooling surfaces.