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Abstract We compare the conditions leading to the stabilization of turbulent methane air and oxy-flames in the outer recirculation zone (ORZ) of a lean premixed acoustically decoupled swirl combustor. The appearance of a flame in the ORZ is an important flame macrostructure transition that was previously shown to be associated with the onset of thermo-acoustic instability under acoustically coupled conditions. We find that, when similar bulk flow conditions are imposed in the ORZ, the transition is governed by the extinction strain rate and can occur at different adiabatic flame temperature and unstretched laminar burning velocity. First, we show that an important non-dimensional parameter characterizing the flow in the ORZ, that is the Strouhal number associated with the azimuthal ORZ spinning frequency, is independent of the Reynolds number and has the same constant value in air and oxy-combustion ( S t = f O R Z . D i n U i n , b u l k ≈ 0.12 ). This has the important implication that the inlet velocity is a more relevant parameter choice than the inlet Reynolds number in order to maintain similar flow conditions in the ORZ. Next, by comparing the extinction strain rates – computed at the measured ORZ temperature – we show the existence of a single correlation between the inverse of the ORZ spinning frequency (taken as a characteristic ORZ flow time) and the inverse of the extinction strain rate (taken as a characteristic flame time) valid for both air and oxy flames and delimiting the regions of existence of different flame macrostructures.