Conditional analysis is performed on statistical behavior of the flamelet characteristics at the leading edge and through the flame brush of incompressible turbulent premixed flames. The effective Lewis number is equal to unity with no stretch effect associated with differential diffusion. It is shown that the flamelet thickness, delta(f), is a crucial parameter to determine the local displacement speed, S-d, as well as the global turbulent burning velocity, S-T. There hold asymptotic relationships for S-T and conditional velocities at the leading edge in the statistically steady state. S-d is correlated with finite delta(f) not in terms of stretch, but through independent effects of tangential strain rate and curvature. S-d and delta(f) show strong correlations with curvature due to significant influence of tangential flux, while they show weak correlations dependent on the location in a flamelet with tangential strain rate. Flamelets tend to thicken according to the gradient of S-d due to focusing or defocusing of c transport for both positive and negative curvatures. The range of S-d is scaled by the tangential component, S-dt, with additional contribution of the normal S-dn component due to delta(f) varying with curvature. Variation of S-dt is given in terms of the product of curvature and molecular diffusivity in the reaction-diffusion layer retaining a relatively invariant structure under turbulence. The stretched laminar flamelet model needs to be complemented by the additional effects of tangential flux and variation of finite delta(f) in fully turbulent premixed flames. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.