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An experimental study of methane, propane and dimethyl ether (DME) pre-mixed flames propagating in a quasi-two-dimensional Hele-Shaw cell placed horizontally is presented in this paper. The flames are ignited at the open end of the combustion chamber and propagate towards the closed end. Our experiments revealed two distinct propagation regimes depending on the equivalence ratio of the mixture as a consequence of the coupling between the heat-release rate and the acoustic waves. The primary acoustic instability induces a small-amplitude, of around 8 mm, oscillatory motion across the chamber that is observed for lean propane, lean DME, and rich methane flames. Eventually, a secondary acoustic instability emerges for sufficiently rich (lean) propane and DME (methane) flames, inducing large-amplitude oscillations in the direction of propagation of the flame. The amplitude of these oscillations can be as large as 30 mm and drastically changes the outline of the flame. The front then forms pulsating finger-shaped structures that characterize the flame propagation under the secondary acoustic instability. The experimental setup allows the recording of the flame propagation from two different points of view. The top view is used to obtain accurate quantitative information about the flame propagation, while the lateral view offered a novel three dimensional perspective of the flame that gives relevant information on the transition between the two oscillatory regimes. The influence of the geometry of the Hele-Shaw cell and of the equivalence ratio on the transition between the two acoustic-instability regimes is analyzed.