Burning carbon-free fuels such as hydrogen in gas turbines promise power generation with minimal emissions of greenhouse gases. A two-stage sequential combustor architecture with a propagation-stabilized flame in the first stage and an auto-ignition-stabilized flame in the second stage allows for efficient combustion of hydrogen fuels. However, interactions between the auto-ignition-stabilized flame and the acoustic modes of the combustor may result in self-sustained thermoacoustic oscillations, which severely affect the stable operation of the combustor. In this paper, we study an “intrinsic” thermoacoustic feedback mechanism in which acoustic waves generated by unsteady heat release rate oscillations of the auto-ignition front propagate upstream and induce flow perturbations in the incoming reactant mixture, which, in turn, act as a disturbance source for the ignition front. We first perform detailed reactive Navier–Stokes (direct numerical simulation (DNS)) and Euler computations of an auto-ignition front in a one-dimensional setting to demonstrate the occurrence of intrinsic instability. Self-excited ignition front oscillations are observed at a characteristic frequency and tend to become more unstable as the acoustic reflection from the boundaries is increased. The Euler computations yield identical unsteady ignition front behavior as the DNS computations, suggesting that diffusive mechanisms have a minor effect on the instability. In the second part of this work, we present a simplified framework based on the linearized Euler equations (LEE) to compute the sound field generated by an unsteady auto-ignition front. Unsteady auto-ignition fronts create sources of sound due to local fluctuations in gas properties, in addition to heat release oscillations, which must be accounted for. The LEE predictions of the fluctuating pressure field in the combustor agree well with the DNS data. The findings of this work are essential for understanding and modeling thermoacoustic instabilities in reheat combustors with auto-ignition-stabilized flames.