The interaction of acoustic waves with a planar counterflow flame is investigated numerically employing a detailed kinetic model and one-step global kinetic models. The mathematical formulation of quasi-one-dimensional fully unsteady laminar counterflow flames is presented and the governing equations are integrated numerically based on a MacCormack predictor–corrector scheme with second-order accuracy in space. Navier–Stokes characteristic boundary conditions are implemented to accurately represent perfect and partial reflection of acoustic waves at the boundaries. For well-resolved simulations, the occurrence of self-excited flame–acoustics instabilities is analysed in both non-premixed and premixed flames for a range of flow strain rates and flame locations, and employing two finite-rate kinetic models. Unlike the detailed kinetic model, one-step global models with large activation energy and overall reaction order greater than unity promote the amplification of acoustic pressure fluctuations in counterflow non-premixed flames. In contrast, premixed counterflow flames exhibit flame–acoustics instabilities with both kinetic models. While previous unsteady counterflow studies required external perturbations, the resonant unsteady phenomena predicted in this study are self-sustained under favourable boundary conditions. Detailed analyses of the characteristic time scales associated with convection, diffusion, chemistry and acoustics are presented to provide a better understanding of the exact coupling mechanisms.