Unsteady flame propagation in a tube is examined by introducing a mean velocity variation larger than the burning velocity to a stabilized flame for a period longer than the reaction time scale. In our previous work, stabilized propane-air flames were classified as either one-dimensional or two-dimensional flames. The eventual extinction during the velocity increase was categorized as either acoustic extinction or boundary layer extinction. In this work, the effects of a nonunity Lewis number were estimated through experiments with a methane-air flame; the eventual extinction during the velocity decrease was investigated in more detail; and the growth of the extinction boundary layer was analyzed with a transient one-dimensional model of the flame stretch. In our experiments, the Lewis number did not affect the existence or characteristics of the critical velocity and the characteristic time for boundary layer extinction. An additional critical velocity was found, however, for acoustic extinction when the Lewis number was smaller than unity. In the transient one-dimensional model, the velocity transition along the flame was calculated with a continuity equation and an axial momentum equation. The spatial gradient of the burning velocity and the extinction criterion were simplified with the experimental results and some theoretical studies. The analysis shows that the unsteady flame stretch at the flame edge during a large axial velocity variation is the prevailing cause of the growth of the extinction boundary layer. These results provide some evidence that flame stretch affects the behavior of the flame edge; they also suggest the cause of the finger flame. The findings help explain the unsteady behavior of premixed flames near a flammability limit. (C) 2003 The Combustion Institute. Published by Elsevier Inc. All rights reserved.