Numerical simulations are carried out to study flame propagation in laminar stratified fuel-air mixtures. Studies are carried out in hydrogen-air and methane-air mixtures. A 30-species 184-step skeletal mechanism is employed for methane oxidation and a 9-species 21-step methanism for hydrogen oxidation. The study seeks to provide an improved understanding of possible differences in the local flame speed at an equivalence ratio in the compositionally stratified mixture from the speed in a homogeneous mixture at the same equivalence ratio. Flame speed and temperature profiles are evaluated and compared with corresponding values for homogeneous mixtures. As shown in prior experimental work, the numerical results suggest that when the flame propagates from a richer mixture to a leaner mixture, the flame speed is faster than the corresponding speed of the homogeneous mixture. The flame zone thickness is observed to be thinner in the stratified mixture resulting in sharper gradients. As a result, the rate of diffusion of heat and species increases resulting in increased flame speed. The effects become more pronounced in leaner mixtures. The stratification gradient influences the results with shallower gradients showing less difference in flame speeds between stratified and homogeneous mixtures. The comparative effect of thermal diffusion and species diffusion on the differences in flame speed is studied. It is shown that the species diffusion effect is more important. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.