This paper presents descriptions and analysis of novel acoustic phenomena that have been observed during the combustion of particle clouds in flame tubes in a reduced gravity environment. It has been found that flame propagation is steady for fuel-rich particle mixtures. However, for near-stoichiometric mixtures of fuel and air, the flame propagates in an unsteady “chattering” or vibratory fashion accompanied by high amplitude periodic pressure oscillations. A longitudinal mode combustion instability analysis of the system is formulated to explain this behavior. Predictions from the model are in good agreement with experimentally obtained data. In particular, the oscillation frequency is well predicted and it is shown that stoichiometrically rich particle mixtures may adversely affect the excitation of the flame-acoustic instability and contribute to the observed disappearance of chattering flames for fuel-rich mixtures.