Premixed flame propagation from a mixture of equivalence ratio phi(1) to one of phi(2) is studied using a flame code with adaptive grids. The traditional definition of laminar flame speed based on the upstream unburned mixture density is found not to be appropriate because that would give an over- or under- shoot in flame propagation speed. The flame properties, however, could be characterized by an effective equivalence ratio phi(eff) so that an equivalent homogeneous flame at phi(eff) may be found for which the CO concentration at the peak of the heat release rate is the same as that in the instantaneous stratified flame. There is a delay between when the flame edge (the beginning of the flame preheat zone) arrives at the equivalence ratio gradient, and when the flame character (exemplified by the instantaneous value of phi(eff)) begins to change. Then the flame burns through the gradient region with an average speed approximately equals to an average of the flame speeds at phi(1) and phi(2).