Particulate material to be calcined is conditioned and then introduced into a stream of flue gases which transport the material along a sloping drying duct while drying the material. The dried material is then introduced into the same stream of flue gases upstream of the drying duct, and the flue gases transport the dried material along a sloping preheating duct while preheating the material. The preheated material is fed tangentially into the lower end of a vertical calcine reactor and calcined product is withdrawn tangentially from the upper end of the reactor. The flue gases used for drying and preheating are produced in the calcine reactor and are cooled during the drying and preheating.