NOVELTY - Producing methane comprises: collecting combustion exhaust gas from a hydrocarbon fuel combustion process; separating oxygen from carbon dioxide to generate carbon dioxide-rich anaerobic exhaust gas fraction (12); feeding the carbon dioxide-rich anaerobic exhaust gas fraction to a fermentation mixture (10) containing methanogenic microorganisms; feeding a reduced substrate to the fermentation mixture; and producing a biogas comprising methane in the mixture; fractionating the biogas into methane- and carbon dioxide-rich fraction; and processing the methane-rich fraction for energy.    USE - The method is useful for producing methane, preferably ethanol, higher alcohols or diesel fuel. The method is useful to decrease emission of carbon dioxide from combustion of fossil fuels or other hydrocarbons and to enhance the efficiency of methane production from anaerobic biodigesters.    ADVANTAGE - The method: avoids a runaway greenhouse effect; decreases carbon dioxide release from fossil fuel use; increases energy yield from fossil fuel combustion; or increases the yield of renewable energy.    DETAILED DESCRIPTION - Method of producing methane comprises: (a) collecting combustion exhaust gas from a hydrocarbon fuel combustion process; (b) separating oxygen from carbon dioxide in the exhaust gas to generate a carbon dioxide-rich anaerobic exhaust gas fraction (12); (c) feeding the carbon dioxide-rich anaerobic exhaust gas fraction to a fermentation mixture (10) containing methanogenic microorganisms; (d) feeding a reduced substrate, which is hydrogen and/or organic material, to the fermentation mixture; (e) producing a biogas comprising methane in the fermentation mixture by the anaerobic fermentation of methanogenic microorganisms; (f) fractionating the biogas into a methane-rich fraction and a carbon dioxide-rich fraction; and (g) processing the methane-rich fraction for energy, where feeding the carbon dioxide-rich anaerobic exhaust gas fraction to the fermentation mixture increases methane production in the fermentation mixture.    DESCRIPTION OF DRAWING(S) - The diagram shows the operation of a biodigester producing a methane-containing biogas from a reduced substrate and a carbon dioxide-rich anaerobic exhaust gas.    Fermentation mixture (10)    Digester (11)    Carbon dioxide-rich anaerobic exhaust gas fraction (12)    Organic material (14)    Gas bubbles. (15)