This numerical study investigates the linear and non-linear flame dynamics in the second stage of a sequential combustor, with methane fuel injection into vitiated hot gas. It focuses on the heat release rate response of the sequential flame to entropy waves. The response is shown to be very sensitive to small changes in operating condition and excitation amplitude. One-dimensional (1-D) flame simulations were performed to identify transitions between three combustion regimes: autoignition, flame propagation and flame propagation assisted by autoignition. Three-dimensional (3-D) large eddy simulations (LES) were performed for two configurations: one that includes the fuel injector and the mixing section, and one with a perfectly premixed inlet. An analytically reduced chemistry (ARC) mechanism, which allows to account for autoignition chemistry, was used in combination with the dynamic thickened flame (DTF) model. For certain conditions, local autoignition events occur upstream of the flame in the advected "hot" streamwise strata that result from the inlet modulation. These auto-ignited kernels get convected downstream and impinge on the stabilized flame front leading to a sudden increase of heat release rate followed by an abrupt decrease due to flame front merging. This is identified as the driving mechanism for the onset of non-linear flame response characterised by high transfer function gains. In particular, this work shows that the gain of the flame describing function increases beyond a certain threshold of the excitation amplitude. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.