The thermoacoustic stability of velocity sensitive premixed flames is investigated. A causal representation of the flow-flame-acoustic interactions reveals a flame-intrinsic feedback mechanism. The feedback loop may be described as follows: An upstream velocity disturbance induces a modulation of the heat release rate, which in turn generates an acoustic wave traveling in the upstream direction, where it influences the acoustic velocity and thus closes the feedback loop. The resonances of this feedback dynamics, which are identified as intrinsic eigenmodes of the flame, have important consequences for the dynamics and stability of the combustion process in general and the flame in particular. It is found that the amplification of acoustic power by flame-acoustic interactions can reach very high levels at frequencies close to the intrinsic eigenvalues due to the flame-internal feedback mechanism. This is shown rigorously by evaluating the "instability potentiality" from a balance of acoustic energy fluxes across the flame. One obtains factors of maximum (as well as minimum) power amplification. Based on the acoustic energy amplification, the small gain theorem is introduced as a stability criterion for the combustion system. It allows to formulate an optimization criterion for the acoustic characteristics of burners or flames without regard of the boundary conditions offered by combustor or plenum. The concepts and methods are exemplified first with a simplistic n - tau model and then with a flame transfer function that is representative of turbulent swirl burners. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.