Results are presented to examine the combustion of acid gas (H2S and CO2) in hydrogen-fueled flames using a mixture of oxygen and nitrogen under Claus conditions (Φ = 3). Specifically the effect of oxygen enrichment in the above flames is examined. The compositions of acid gas examined are100% H2S and 50% H2S/50% CO2 with different percentages of oxygen enrichment (0%, 19.3% and 69.3%) in the oxygen/nitrogen mixtures. The results revealed that combustion of acid gas formed SO2 wherein the mole fraction of SO2 increased to an asymptotic value at all the oxygen concentrations examined. In addition, increase in oxygen enrichment of the air resulted in increased amounts of SO2 rather than the formation of more desirable elemental sulfur. In case of 50% H2S/50% CO2 acid gas, carbon monoxide mole fraction increased with oxygen enrichment which is an indicator to the availability of additional amounts of oxygen into the reaction pool. This gas mixture resulted in the formation of other sulfurous–carbonaceous compounds (COS and CS2) due to the presence of carbon monoxide. The results showed that the rate of COS formation increased with oxygen enrichment due to the availability of higher amounts of CO while that of CS2 reduced. The global reactions responsible for this observed phenomenon are presented.