The formulation of counterflow, quasi onedimensional, unsteady, compressible conservation equations are presented, together with the decomposition of pressure into mean pressure along the axis of symmetry, unsteady or acoustic (in axial direction) and radial components. The discretized equations are integrated numerically using a Mac-Cormack predictor-corrector scheme. The Navier-Stokes characteristic boundary conditions are used to accurately represent the perfectly reflecting and partially reflecting boundary conditions. For wellresolved simulations, the occurrence of self-excited flame-acoustic instabilities is analyzed for a range of flow strain rates and two finite-rate kinetic models. It is shown that for identical flow strain rates, the one-step global model promotes growth of the unsteady pressure, while the detailed kinetic model does not. Detailed analyses of the characteristic time scales are presented in an attempt to better understand the exact coupling mechanism.