Process for desulphurizing flue gas comprising gaseous SO 2 and converting SO 2 into anhydrous CaSO 4, comprising the steps of • reacting the SO 2 -comprising flue gas with inflowing solid Ca 2 and/or solid CaO in a first fluidised bed reactor which first reactor is operated at higher temperature, wherein • an effluent flue gas stream from the first fluidised bed reactor is then used to directly contact solid Ca 2 and/or solid CaO in a lower temperature absorber unit which absorber unit is a second fluidised bed reactor, and • wherein effluent solid recirculating from said second fluidised bed reactor is at least partly removed for being used as said inflowing solid for the first fluidised bed reactor, and • finally harvesting anhydrous CaSO 4 from said first fluidised bed reactor, and • the effluent flue gas from the first fluidised bed reactor is transported by first connecting elements to the gas inlet of the second fluidised bed reactor, and the effluent solids removed from the second fluidised bed reactor are transported by second connecting elements to the first fluidised bed reactor, characterized in that • the effluent flue gas stream from the first fluidised bed reactor is used to heat gas-fluidised, solid Ca 2 and/or solid CaO streaming towards the first fluidised bed reactor from the second fluidised bed reactor in at least one heat exchanger element operating in counterstream mode, and • the heat exchange is mediated in between the effluent solids and the effluent waste gas by heat exchange between the first connecting elements for the effluent waste gas from the first fluidised bed reactor and the second connecting elements for the effluent solids from the second fluidised bed reactor, and • the at least one heat exchanger element is an indirect heat exchanger element operating in counterstream mode. • reacting the SO 2 -comprising flue gas with inflowing solid Ca 2 and/or solid CaO in a first fluidised bed reactor which first reactor is operated at higher temperature, wherein • an effluent flue gas stream from the first fluidised bed reactor is then used to directly contact solid Ca 2 and/or solid CaO in a lower temperature absorber unit which absorber unit is a second fluidised bed reactor, and • wherein effluent solid recirculating from said second fluidised bed reactor is at least partly removed for being used as said inflowing solid for the first fluidised bed reactor, and • finally harvesting anhydrous CaSO 4 from said first fluidised bed reactor, and • the effluent flue gas from the first fluidised bed reactor is transported by first connecting elements to the gas inlet of the second fluidised bed reactor, and the effluent solids removed from the second fluidised bed reactor are transported by second connecting elements to the first fluidised bed reactor, characterized in that • the effluent flue gas stream from the first fluidised bed reactor is used to heat gas-fluidised, solid Ca 2 and/or solid CaO streaming towards the first fluidised bed reactor from the second fluidised bed reactor in at least one heat exchanger element operating in counterstream mode, and • the heat exchange is mediated in between the effluent solids and the effluent waste gas by heat exchange between the first connecting elements for the effluent waste gas from the first fluidised bed reactor and the second connecting elements for the effluent solids from the second fluidised bed reactor, and • the at least one heat exchanger element is an indirect heat exchanger element operating in counterstream mode.