The hetero-/homogeneous chemistry interactions during the catalytic partial oxidation (CPO) of methane were investigated numerically in rhodium-coated cylindrical channels using axisymmetric simulations with detailed catalytic and gas-phase chemistries, conjugate heat transfer in the solid wall and detailed transport. Simulated conditions spanned pressures 1–25 bar, methane-to-air equivalence ratios 2.5–4.0, inlet temperatures 300–900 K and channel diameters 0.5–2.0 mm. The formation of vigorous flames in the oxidation zone of the CPO reactor was promoted as the pressure, inlet temperature and channel diameter increased. The catalytic pathway induced a strong radial stratification of the reactant and temperature distributions over the homogeneous combustion zones. This in turn resulted in flames spatially confined to the channel core, such that the catalytic wall temperature was only modestly affected by the flames (∼25 K wall temperature rise due to the flame presence), a result highly desirable for the reactor thermal management and for the catalyst thermal stability. Even when strong flames were formed, combined hetero-/homogeneous combustion persisted over the entire axial extent of the flames. The deficient oxygen reactant leaked through the flame zones and was subsequently converted catalytically on the channel walls, with the oxygen leakage increasing as the channel diameter, pressure, and inlet temperature decreased. Extensive parametric simulations delineated the regimes of operating conditions and geometrical parameters (pressure, inlet temperature, equivalence ratio and channel diameter) for which gas-phase combustion could not be ignored during methane CPO over rhodium. It was shown that for practical power generation systems (pressures and inlet temperatures above 15 bar and 600 K, respectively) gaseous chemistry could not be neglected and offered the benefit of reducing the extent of the oxidation zone and hence the overall reactor length.