The structure and extinction characteristics of counterflow diffusion flames with flame radiation and nonunity Lewis numbers of the fuel and oxidant are examined using multiscale asymptotic theory, and a model expressed in terms of the jump relations and reactant leakages with the proper consideration of the excess enthalpy overlooked in previous analyses is developed. The existence of the dual extinction limits in the presence of radiative heat loss, namely the kinetic limit at small Damkohler number (high stretch rate) and the radiative limit at large Damkohler number (low stretch rate), are identified. It is found that the former is minimally affected by radiative loss, while a substantial amount of heat loss is associated with the radiative limit. Reactant leakage, however, is the root cause for both limits. The influence of radiative loss on the extinction Damkohler numbers is found to be through its effects on the flame temperature, the excess enthalpy, and the reduced extinction Damkohler number. At both extinction limits, the contribution from the flame temperature is always important and dominant. The contributions from the other two, however, could be important in some special cases. At small Le(F), the contribution from the reduced extinction Damkoller number is large and even dominant under small radiative loss. The contribution from the excess enthalpy is important for small Le(O) and it may be comparable to the contribution from the flame temperature when radiative loss is small. Thus, overlooking the excess enthalpy in previous analyses may have resulted in rather large error in the predicted extinction Damkohler numbers, especially the kinetic one. (c) 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.