Within the framework of slowly varying flames we derive an equation for the burning rate of a flame in a strained flow field under near-stoichiometric conditions. Our expression exhibits a nonlinear dependence of flame speed on the strain rate and depends on the mixture＇s equivalence ratio as well as two distinct Lewis numbers, corresponding to the fuel and oxidant. For a strained flame, the rate at which a given reactant reaches the reaction zone is strongly affected by its molecular diffusivity. We demonstrate that it is possible for the reactant which is initially in excess to be entirely consumed by the reaction, while the initially deficient reactant leaks through. This is shown to have important implications on the extinction characteristics of the flame. We calculate burning velocities using parameter values typical of several hydrocarbon-air and hydrogen-air mixtures and show that our predictions are in good agreement with experimental results.