A simple model of a flame from propagating through a fuel-rich droplet-vapor-air mixture is presented. An arbitrary polydisperse size distribution of droplets in the spray is allowed. The droplets are permitted to vaporize at a finite rate so that their interaction with and possible traversal of the flame front is accounted for. Steady-state solutions are established by means of large activation energy asymptotics. An analysis of instability to transverse perturbations is then carried out in order to determine neutral stability boundaries. Two initial droplet size distributions having the same Sauter mean diameter (SMD) are considered. One is initially quasi-monodisperse (A), whereas the second is bimodal (B). It is found that the onset of flame cellularization is sensitive to the initial droplet size distribution in the spray. Specifically, under certain operating conditions, the flame resulting from distribution A is cellular, whereas that of distribution B is stable. Under other conditions, in which both spray flames are unstable, the cellular structure of flame A is found to be finer than that of flame B. These results indicate that use of the SMD to characterize a spray in the context of cellular flame instability may lead to mistaken conclusions. However, the location of the pulsating stability boundaries was found to be rather insensitive to the initial droplet distribution and, indeed, to the presence of the droplets. In addition, it lay beyond the practical range of Lewis numbers relevant to these rich flames.