A method of and a plant for combusting carbonaceous fuel, the method including the steps of introducing particulate oxygen selective sorbent, such as a perovskite type material, into an adsorption reactor of the combustion plant to form a first particle bed in the adsorption reactor, fluidizing the first particle bed by an oxygen-containing first fluidizing gas to adsorb oxygen from the fluidizing gas to the sorbent, conveying oxygen-rich sorbent from the adsorption reactor to a combustion reactor of the combustion plant to form a second particle bed in the combustion reactor, fluidizing the second particle bed by an oxygen-deficient second fluidizing gas to desorb oxygen from the sorbent, so as to produce free oxygen gas, and introducing carbonaceous fuel into the combustion reactor to oxidize the fuel with the free oxygen gas.