This paper presents an experimental investigation into mode-transitions observed in a 50-kW, atmospheric pressure, backward-facing step combustor burning lean premixed C3H8/H-2 fuel mixtures over a range of equivalence ratios, fuel compositions and preheat temperatures. The combustor exhibits distinct acoustic response and dynamic flame shape (collectively referred to as "dynamic modes") depending on the operating conditions. We simultaneously measure the dynamic pressure and flame chemiluminescence to examine the phase between pressure (p') and heat release fluctuations (q') in the observed dynamic modes. Results show that the heat release is in phase with the pressure oscillations (0(qp) approximate to O) at the onset of a dynamic mode, while as the operating conditions change within the mode, the phase grows until it reaches a critical value 0(qp) = 0(c), at which the combustor switches to another dynamic mode. According to the classical Rayleigh criterion, this critical phase (0(c)) should be pi/2, whereas our data show that the transition occurs well below this value. A linear acoustic energy balance shows that this critical phase marks the point where acoustic losses across the system boundaries equal the energy addition from the combustion process to the acoustic field. Based on the extended Rayleigh criterion in which the acoustic energy fluxes through the system boundaries as well as the typical Rayleigh source term (p'q') are included, we derive an extended Rayleigh index defined as R-e = 0(qp)/0(c) which varies between 0 and 1. This index, plotted against a density-weighted strained consumption speed, indicates that the impact of the operating parameters on the dynamic mode selection of the combustor collapses onto a family of curves, which quantify the state of the combustor within a dynamic mode. At R-e = 0, the combustor enters a mode, and switches to another as R-e approaches 1. The results provide a metric for quantifying the instability margins of fuel-flexible combustors operating at a wide range of conditions. (C) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.