In this paper the extinction of laminar, premixed flames fed with a mixture of methane and hydrogen is numerically modeled in unsteady conditions. The aim of the work is to better understand how the oscillations of the flow field and the addition of hydrogen to the fuel mixture affect the extinction limits of the flame. For this purpose, numerical simulations of laminar, premixed, symmetric counter-flow flames were performed using a detailed kinetic mechanism (similar to 80 species and 1400 reactions). Steady-state conditions were first analyzed and the numerical results were compared with the experimental measurements with satisfactory agreement, showing that the main effect of hydrogen addition is to increase the characteristic extinction limits of the flame. Then, harmonic oscillations were imposed on the inlet velocities, in order to study the response of the flame (in terms of temperature and species) to the unsteadiness of the flow field. The results clearly showed that, as long as the averaged strain rate is smaller than the steady state strain rate, the oscillating flames can always survive instantaneous high strain rates for sufficiently high frequencies. Moreover, the unsteady flames are able to survive to instantaneous strain rates well beyond the corresponding steady-state extinction conditions, especially when the frequency of oscillations is large. Eventually, it was found that the flame behavior under unsteady conditions can be effectively explained using the Stokes' number (i.e. the ratio between the frequency of imposed oscillations and the strain rate of the flame), a dimensionless parameter comparing the characteristic times of the flame and of the imposed disturbances. (C) 2013 Elsevier Ltd. All rights reserved.