Reheat flames are mainly stabilized by autoignition processes. In this paper their unsteady response to temperature fluctuations is investigated. To this end, a simple one dimensional duct is considered as an analytic surrogate model of a reheat combustion chamber. A chemistry-based correlation for the autoignition delay time is used to predict the flame position. In order to analyze the flame response to temperature fluctuations, the inlet boundary condition is harmonically excited. Depending on the amplitude and frequency of excitation, nonlinear phenomena are observed, in particular the co-existence of multiple flame fronts at different axial locations. The analytic formulation of the problem allows us to predict the onset of nonlinearities and to evaluate maps separating the linear from the nonlinear behavior, as function of the system parameters. Amplitude and frequency thresholds triggering different nonlinear properties of the system are identified. Verification of the obtained results for different excitation states is made by comparison to previously conducted Large Eddy Simulations of a simplified reheat combustor geometry represented by a backward-facing step. The simplified model is able to correctly predict the appearance of nonlinear phenomena as observed in the simulations suggesting that the governing factors are well represented. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.