The interaction of acoustic waves with planar methane–air counterflow premixed flames is investigated numerically employing a detailed and several global kinetic models. The quasi one-dimensional fully unsteady governing equations for laminar counterflow flames are integrated based on a MacCormack predictor–corrector scheme with the implementation of Navier–Stokes characteristic boundary conditions. For well-resolved simulations, the occurrence of self-excited flame–acoustics instabilities is analyzed in both twin-premixed and single-premixed counterflow flames for a range of flow strain rates and flame locations. While previous unsteady counterflow work required external perturbations, the resonant unsteady phenomenon predicted in this study is self-sustained under favorable boundary conditions. It is shown that the acoustic response of the flame with the detailed model varies depending on geometry and phase effects. In contrast, one-step global models with large activation energy (126kJmol⁻¹) always promote the amplification of acoustic pressure fluctuations. However, two-step global models developed with the same activation energy for the initiation reaction and with zero activation energy for the second propagation reaction exhibit a wide range of flame–acoustics interactions, depending on the distribution of heat release among the two reactions. Detailed analyses of the difference in phase between oscillatory pressure and velocity due to flame location, as well as of characteristic time-scales associated with transport, chemistry and acoustics are presented to provide a better understanding of the exact coupling mechanisms.