The heterogeneous and homogeneous combustion of C3H8/O2/N2 mixtures over Rh was investigated at pressures 1-6 bar, catalyst surface temperatures 680-1100 K and C3H8-to-O2 equivalence ratios 0.25-0.52. Non-intrusive laser-based measurements were applied in a channel-flow catalytic reactor and involved 1-D Raman spectroscopy of major gas-phase species across the channel boundary layer for assessing the catalytic reactivity and planar laser induced fluorescence (PLIF) of the OH radical for monitoring homogeneous combustion. Simulations were carried out with a 2-D numerical code that included detailed hetero-/homogeneous chemical reaction mechanisms. By comparing the Raman-measured and predicted transverse profiles of the limiting C3H8 reactant, the suitability of a detailed surface reaction mechanism was initially evaluated and subsequently a one-step reaction was constructed, which was applicable for the C3H8 total oxidation over Rh at pressures 1 to 6 bar. The catalytic reactivity of C3H8 over Rh displayed a ∼p^0.14 pressure dependence, which was substantially lower than a previously reported ∼p^0.70 dependence over Pt. The weak pressure dependence of the C3H8 reactivity on Rh suggested caution when selecting catalysts for high-pressure power systems (recuperative microreactors, small-scale turbines) fueled with C3H8 or LPG (liquefied petroleum gas). Comparisons of PLIF-measured and predicted distributions of the OH radical indicated that the employed gas-phase reaction mechanism captured the onset of homogeneous ignition at pressures greater than or equal to 3 bar as well as the ensuing flame shapes. Predicted and measured homogeneous ignition distances agreed within 2.5% at 6 bar. With decreasing pressure, the predictions yielded gradually increasing but still modest underpredictions (up to 11.2% at 3 bar) of the homogeneous ignition distances. The key gas-phase reactions affecting homogeneous combustion at various pressures were finally identified.