Recent experimental work by Levy  has revealed a pulsating mode of diffusional combustion for a Burke-Schumann flame set-up with fuel spray injection. The gross flame pulsations are accompanied by the production of small flamelets at the tip of the main flame that break off and disappear downstream. In an attempt to uncover the mechanism responsible for these unsteady phenomena the evolution of a Burke-Schumann type of spray diffusion flame is examined theoretically. Full representation of transport, spray and combustion is allowed through use of nonunity Lewis numbers for the gaseous components, local pointwise multisize droplet distribution for the spray and a finite chemical Damkohler number based on a single global chemical reaction. It is found that under certain operating conditions the transient behaviour of the spray flame exhibits the phenomenon of flame separation, even though a steady state is ultimately attained. The local polydispersity of the spray is shown to be one of the factors affecting the appearance of the separated flamelet.