A computational study is performed to investigate the effects of mixture composition oscillations on a strained premixed methane/air flame. The problem is of practical relevance in direct-injection spark-ignition (DISI) engines and gas-turbines, in which premixed flames propagate through temporally and spatially stratified mixture field. The primary focus of the study is to identify the dynamic flammability limit, defined as the minimum instantaneous mixture equivalence ratio that can sustain flame propagation. It is shown that the difference between the dynamic and steady flammability limits, φt - φs, represents the extension of the flammability limit under unsteady condition, and is a function of the mean strain rate, frequency of oscillation, and mean equivalence ratio. A proper normalization is proposed in order to scale the dynamic flammability limit extension as a function of a nondimensional frequency. As an improvement from previous studies, the use of time scale based on the actual flame thickness and speed represents the correct physical time and length scales involved in the process, thereby yielding a good collapse of the data. As a related subject, a universal extinction criterion for unsteady flames is proposed based on the local Karlovitz number defined as the ratio of the local reaction time to the characteristic flow time. The results show that the maximum local Karlovitz number at the dynamic flammability limit is approximately constant, irrespective of strain rate, mean equivalence ratio, and frequency of oscillation. The results thus extends earlier studies on the local Karlovitz number in steady flame extinction.