The nature of premixed methane-air flames stabilised on a symmetric, plane sudden-expansion has been examined in terms of wall pressures and the chemiluminescence of the CH radical. Large-amplitude acoustic oscillations at the half-wave frequency of the entire duct were observed at high velocities and with near-stoichiometric mixtures, and instabilities with much lower-frequencies close to the lean and rich extinction limits. The emphasis is on these near-limit instabilities and, due to the asymmetry of the plane flow, the experiments were extended to round ducts in which the flammability and stability limits were similar to those in the plane duct. The branches of flame behind the steps of the plane expansion extinguished non-simultaneously, and gave rise to low-frequency flapping oscillations immediately prior to extinction of the first of these, and the remaining branch gave rise to lateral oscillations prior to its extinction. The oscillations were associated with axial movement of extinction along the shear layer due to the high strain rates close to the step, until the strain rate was sufficiently low and allowed upstream propagation of the flame through the recirculation region. The flames in the round duct gave rise to oscillations of the same nature. The frequency of the oscillations increased with flow velocity and flame speed, and the amplitude with heat release and much more with constriction of the duct exit due to coupling with a bulk-mode of the combustor cavity. These increased amplitudes caused the flammability limits to narrow due to the consequently higher strain rates and have implications for gas turbine operation.