Interactions between turbulent mixing and finite-rate chemistry effects leading to highly nonequilibrium behavior of nonpremixed flames in incompressible, homogeneous turbulence are simulated by utilizing the linear-eddy model (LEM). Computations reveal that as turbulent mixing increases the local scalar dissipation rate, the mean temperature and reaction rate decrease rapidly at the flame location and, depending on the activation energy, the flame either reignites or extinguishes. The LEM results are also compared to predictions from the conditional moment closure (CMC) model and reveal interesting differences between these models near conditions of flame extinction. Specifically, for the chemistry under consideration and within the context of the comparisons to the LEM simulations, the results highlight the importance in the CMC approach of modeling the conditionally averaged mixture-fraction dissipation rate and accounting for conditional fluctuations in the chemical reaction rate term in nonpremixed combustion systems near extinction.