Carbon dioxide (CO2) emission forms the biggest portion of greenhouse gas emissions known to cause global warming, which can lead to climate change. One of the most widely recommended means of tackling CO2 emission is the carbon capture technique, which includes oxyfuel combustion. In oxyfuel combustion, O-2/CO2 oxidizer mixtures are used to lower the oxy-combustion temperatures to make it suitable for the components of the combustion systems. These oxidizer mixtures, depending upon the relative concentrations of the species, exhibit distinct combustion characteristics. In this study, flame stability of propane-air and propane-oxyfuel combustion is studied in a non-premixed, swirl-stabilized combustor. The combustion of air was compared to two oxyfuel mixtures, namely, oxyfuel I and II, in terms of lean blowout limits. Oxyfuel II and air combustion were also compared in terms of the temperature. Furthermore, the effects of the CO2 dilution level, equivalence ratio, swirl number, and combustor firing rate on oxyfuel flame stability were studied. Results show that, for lean mixtures, the propane-air flame transits from the attached flame to lifted flame before subsequent flame extinction. This is contrary to oxyfuel I and II flames that transit directly from the attached flame to no flame regime at all firing rates studied. Near stoichiometry, however, the oxyfuel flames display distinct flame transitions, including liftup before extinction as a consequence of CO2 dilution at high firing rates. These flame transitions before blowout were observed to be flow-induced. NOx and CO emissions were seen to depend strongly upon air and oxyfuel combustion temperatures. The amount of CO2 required in the oxidizer at blowout was observed to decrease significantly as the equivalence ratio decreases from 1 to 0.9, signifying an enhanced stability at stoichiometric conditions. Further studies revealed that the oxyfuel flames are more stable at the swirl number of 1.0 when compared to 0.6 and 1.5.