The nonlinear response of stretched premixed dames was studied analytically and computationally, with emphasis on the turning point behavior associated with flame extinction. Extending our previous study of the weakly stretched flames exhibiting linear responses, expressions for the nonlinear flame response were derived by using an integral method. For adiabatic flames, the extinction stretch rates were determined by using the global flame parameters extracted from the linear flame response. The predicted flame responses were then compared with computed results for counterflow and inwardly propagating spherical flames, and reasonably good agreements were obtained. The agreement was further improved by taking into account the increase of the effective activation energy with decreasing flame temperature as the flame approaches the extinction state. For nonadiabatic flames, the effect of volumetric heat loss was investigated via the one-dimensional planar flame subject to radiation loss, while the effect of conductive loss was studied via the counterflow flame against an isothermal wall. The formulation holds potential utility in predicting quantitatively accurate flame responses and in its implementation in the modeling of turbulent combustion. (C) 2000 by The Combustion Institute.