Constructive interference between heat release rate and acoustic perturbation is responsible for the growth of acoustic pressure amplitudes, leading to high-amplitude combustion instabilities in combustion systems. This is referred to as the Rayleigh criterion. Even though the knowledge of the heat release acoustic pressure coupling processes is critical in the description of self-excited combustion instabilities, little is known about how the unsteady coupling processes are determined in response to the variation of time and length scales of acoustic and convective waves present in turbulent reacting flow fields. To address this issue, we performed a large number of measurements of self-excited instabilities, using two different tunable gas turbine combustors, over a wide range of operating conditions. The initiation, evolution, and saturation of pressure disturbances in swirl-stabilized combustion systems were systematically investigated by integrated analyses of pressure-heat release-velocity feedback coupling processes. It was found that self-excited combustion instabilities are governed by the Rayleigh criterion over the entire parameter space. We also observed that at certain inlet conditions, high amplitude velocity and heat release fluctuations coexist even without pressure-heat release coupling, meaning that the Rayleigh criterion is not necessarily associated with the onset of the self-excited instability. The Rayleigh criterion, however, does play an essential role in the linear to nonlinear transition that is necessary for the system to evolve toward a final state of stable limit cycles. We also found that the presence of equivalence ratio nonuniformities exerts a profound influence on instability feedback mechanisms, and consequently the Rayleigh criterion becomes a weak necessary condition for the occurrence of self-excited instabilities. A feedback mechanism that controls the relationship between velocity and acoustic pressure fluctuations was investigated to understand the effect of swirl number on limit cycle behavior. Acoustic admittance analysis reveals that at sufficiently high disturbance amplitude, nonlinear gas dynamic processes become so significant that the nonlinear saturation behavior cannot be defined by the acoustic velocity amplitude normalized by mean flow velocity. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.