The lean flammability limits of CH4/air and C3H8/air mixtures were numerically determined for a wide range of pressures and unburned mixture temperatures. The main goal was to assess the near-limit flame behavior under conditions of relevance to internal combustion engines. The study included the simulation of freely propagating flames with the inclusion of detailed description of chemical kinetics and molecular transport, radiative losses, and a one-point continuation to solve around singular points as the flammability limit is approached. Results revealed that both pressure and unburned mixture temperature have significant effects on both the lean flammability limit and the attendant limit flame temperature. The lean limit was found to first increase and then decrease with pressure, while the limit temperature decreases with pressure in general, and can be reduced to values as low as 900 K under engine-like conditions. This finding is in contrast with a recently reported limit temperature of 1,900 K under similar initial conditions. Through the use of sensitivity and species consumption path analyses it was shown that the kinetics mechanisms that control the near-limit flame response critically depend on the state of the mixture. Thus, results obtained for flames at near-atmospheric conditions cannot be extrapolated to notably higher values of pressure and unburned mixture temperature. Furthermore, the response of near-limit flames was found to resemble the explosion limits of H2/O2. At low pressures, the main branching is provided by H + O2 = OH + O and the main termination by H + O2 +M = HO2 +M. At high pressures, however, the system branching is controlled instead by the HO2/H2O2 kinetics.