A steady, one-dimensional, low-speed flame propagating in a dilute, monodisperse, sufficiently off-stoichiometric and weakly heterogeneous spray with external heat recirculation, is analyzed using activation energy asymptotics. A prevaporized mode and a partially prevaporized mode of flame propagation are identified. Heat recirculation is achieved by transferring heat through a tube wall within a given distance L. The external heat transfer results bt globally external heat loss and excess enthalpy burning (which is globally adiabatic), respectively, to the spray system with increasing wall temperature. The influences of external heat recirculation and liquid fuel spray on the flammability limit and extinction of spray flames are examined with three parameters, namely, the amount of external heat transfer, the liquid fuel loading, and the initial droplet size. It is found that the extent of flammability is enlarged with increasing liquid loading or decreasing droplet size for lean sprays, while the opposite holds for rich sprays; and that the change of an extinction curve to a curve characterized by blow-off and flashback is controlled by the balance between internal and external heat transfer.