The influence of internal heat transfer induced by dilute compound-drop sprays on one-dimensional pre-mixed flames is investigated using large activation energy asymptotic analysis. In this study, the compound drop is composed of a single water core encased by a shell of fuel. The gasification zones of the shell fuel and the core water affect the flow and flame characteristics. A critical completely pre-vaporized burning condition, (CPB)c, is defined as the whole compound drops finishing vaporization right at the flame and a critical shell pre-vaporized burning condition, (SPB)c, is defined as the shell fuel of compound drops finishing vaporization right at the flame. Under the (CPB)c, and (SPB)c, conditions of lean and rich flames, the flame propagation flux, the critical values of the shell-fuel mass fraction and the initial radius vary with the water-core radius and the liquid loading. For a lean spray flame, compound drops can provide internal heat transfer in the form of heat gain from the shell fuel and heat loss from the core water. The lean spray flame may be strengthened or weakened depending on the net heat transfer. For a rich spray flame, the compound-drop spray always weakens flame propagation. An S-shaped extinction curve occurs for a rich spray flame under the (SPB)c, condition, with a sufficiently heavy liquid loading and a sufficiently large water-core size. (C) 2011 The Combustion Institute. Published by Elsevier Inc. All rights reserved.