The oscillations that occur in ducted plane and round sudden-expansions with combustion of premixed air and methane have been examined for flow conditions which gave rise to large amplitudes corresponding to half-waves. They were present above a minimum flow rate and in a range of equivalence ratios that increased slightly with flow rate and centred around stoichiometry. The periodic roll-up, growth and collapse of combusting vortices downstream of the plane expansion was examined in terms of chemiluminescence images and velocity and temperature measurements synchronised with the pressure oscillation. The periodic heat release and pressure fluctuations were shown to be in phase close to the geometric axis, with the oscillations driven in this region, so that local perturbations were likely to have greatest effect when introduced there. The pressure signals in both ducts were similar so that the flow in the round duct was expected to behave in the same way and, a stream of pulsed methane was thus best able to modify the oscillations when introduced on the axis and close to the expansion plane. Low-frequency oscillations tended to modulate the half-wave with effects that increased with flow rate and, therefore, heat release rate, and stemmed from a combination of the bulk-mode resonance of the upstream cavity and high strain rate in the vicinity of the expansion. The amplitudes of the oscillations in the round duct were controlled by imposing oscillations on the pressure field and heat release at a phase or frequency different from that of the combustion oscillations. Both approaches led to substantial reduction in the amplitude of oscillations at low flow rates, when the modulations were small, but the effectiveness of control deteriorated sharply at the higher flow rates.