Effects of sinusoidal velocity oscillation on counterflow diffusion and premixed flames were computationally investigated as functions of imposed frequency and amplitude and with detailed descriptions of chemistry and transport. The phenomena of interest investigated are: (1) the structural sensitivity of premixed versus diffusion names; (2) the effects of nonequidiffusion on the dynamic response of premixed names; (3) the transient sensitivity of the premixed name burning rate; and (4) the modification of the extinction limits of premixed and diffusion flames. Results show that premixed and diffusion names, respectively, exhibit weak and strong structural responses, that the dynamic response of the premixed dames to mixture nonequidiffusion can be qualitatively disparate For mixtures with Lewis numbers (Le) greater and less than unity, and that the transient burning rate characterized by the spatially integrated reaction rate profile is a better physical representation than that based on the local mass flux. It is further demonstrated that for sufficiently rapid oscillations the flame may not have enough time to extinguish before the how condition again becomes favorable for burning, and as such with increasing frequency a flame can persist beyond the range of the stretch rate in which steady-state flames do not exist, and that for premixed flames with Le > 1, the transient extinction response can be nonmonotonic because of the freely standing nature of the flame and the relatively stronger sensitivity of the name temperature to stretch rate variations.