Method for operating a shaft furnace producing burnt lime, dolomite, magnesia or cement from carbonate-containing raw materials, in particular a method for operating a shaft furnace for producing burnt lime or cement, the shaft furnace having at least one upper raw material inlet zone, at least one central burning zone and at least one lower burnt material outlet zone, characterised by the following measures: a) burning a fuel mixture of a carbon-containing fuel made of methane or methanol and industrially produced tonnage oxygen in the burning zone of the shaft furnace and calcining the carbonate-containing raw material in the burning zone and thereabove, carbon dioxide being additionally introduced into the burning zone and/or the outlet zone of the shaft furnace in each case as a substitute for the nitrogen-containing, atmospheric air customarily used according to the prior art b) removing a waste gas containing at least 80, preferably more than 90, percent by volume of carbon dioxide and resulting from the burning of the fuel mixture, the supplied carbon dioxide and the thermal decomposition of the respective carbonate-containing raw material, at the inlet opening of the raw material inlet zone and leading the waste gas into a waste gas store, the carbon dioxide supplied according to feature a) having been withdrawn from the waste gas store containing the carbon dioxide c) producing methane or methanol in a methanation or methanolation reactor from carbon dioxide supplied to the reactor from the waste gas store and hydrogen supplied to the reactor and leading the methane or methanol into a methane or methanol store d) withdrawing methane or methanol from the methane or methanol store and supplying the methane or methanol as fuel to the burning zone of the shaft furnace e) producing hydrogen and oxygen from water, using water withdrawn from the methanation or methanolation reactor, by electrolysis in an electrolysis system operated by electric current drawn from a plant'sown current-generating plant operated by methane or methanol withdrawn from the methane or methanol store and storing the hydrogen in a hydrogen store and the oxygen in an oxygen store f) feeding hydrogen into the methanation or methanolation reactor from the hydrogen store for carrying out the methanation or methanolation g) feeding oxygen into the burning zone and/or the outlet zone of the shaft furnace from the oxygen store. a) burning a fuel mixture of a carbon-containing fuel made of methane or methanol and industrially produced tonnage oxygen in the burning zone of the shaft furnace and calcining the carbonate-containing raw material in the burning zone and thereabove, carbon dioxide being additionally introduced into the burning zone and/or the outlet zone of the shaft furnace in each case as a substitute for the nitrogen-containing, atmospheric air customarily used according to the prior art b) removing a waste gas containing at least 80, preferably more than 90, percent by volume of carbon dioxide and resulting from the burning of the fuel mixture, the supplied carbon dioxide and the thermal decomposition of the respective carbonate-containing raw material, at the inlet opening of the raw material inlet zone and leading the waste gas into a waste gas store, the carbon dioxide supplied according to feature a) having been withdrawn from the waste gas store containing the carbon dioxide c) producing methane or methanol in a methanation or methanolation reactor from carbon dioxide supplied to the reactor from the waste gas store and hydrogen supplied to the reactor and leading the methane or methanol into a methane or methanol store d) withdrawing methane or methanol from the methane or methanol store and supplying the methane or methanol as fuel to the burning zone of the shaft furnace e) producing hydrogen and oxygen from water, using water withdrawn from the methanation or methanolation reactor, by electrolysis in an electrolysis system operated by electric current drawn from a plant'sown current-generating plant operated by methane or methanol withdrawn from the methane or methanol store and storing the hydrogen in a hydrogen store and the oxygen in an oxygen store f) feeding hydrogen into the methanation or methanolation reactor from the hydrogen store for carrying out the methanation or methanolation g) feeding oxygen into the burning zone and/or the outlet zone of the shaft furnace from the oxygen store.