A method of and apparatus for carrying out an exothermic process in which a combustible-containing solid (e.g. coal shale, pyrite or limestone in combination with fuel oil) are burned in a fluidized-bed reactor with primary and secondary streams of oxygen-containing combustion-sustaining gas (in a volume ratio of 1:20 to 2:1) supplied at different levels so that the primary gas acts as the fluidizing gas. The gas velocities and rate of gas feeds are controlled to provide a mean suspension density above the secondary gas inlet of 10 to 40 kg/m.sup.3. The major portion of solid feed is introduced into the space below the secondary gas inlet which is maintained substantially free of internal fixtures and the effluent gases are separated from the entrained solids which are recycled to the bed. Solids withdrawn from the bed are cooled in a fluidized-bed cooler and the temperature of the bed is maintained constant by the controlled recirculation of cooled solids thereto from the cooler. The gas heated in the cooler is fed to the bed as the secondary gas.