Experimental evidence points to a rich variety of physical scenarios that arise when alaminar flame propagates through a pre-mixture of evaporating liquid fuel and a gaseousoxidant. In this paper new results of time-dependent numerical simulations of richoff-stoichiometric spray flame propagation in a two-dimensional channel are presented. Aconstant density model is adopted, thereby eliminating the Darrieus-Landau instability. Itis demonstrated that there exists a narrow band of vaporization Damkohler numbers (theratio of a characteristic flow time to a characteristic evaporation time) for which theflame propagation is oscillatory. For values outside this range steady state propagationis attained but with a curved (cellular) flame front. The critical range for thenon-steady propagation is also found to be a function of the Lewis number of the deficientreactant.