The distributions across a smooth wall layer of the skewness and flatness factor of the first‐order time derivatives ofuand&ngr;, the longitudinal and normal velocity fluctuations, respectively, and ofu&ngr;, the Reynolds shear stress fluctuations, are compared with the corresponding distributions in a boundary layer over a rough wall. Both the smooth and rough wall boundary layers are nearly self‐preserving under zero pressure gradient conditions. Although the probability density of the square of∂u / ∂t, the time derivative ofu, is reasonably represented by the log‐normal distribution, the skewness and flatness factor of∂u / ∂tin the inner region of the layers are found to remain approximately constant for a turbulence Reynolds numberR &lgr;range 150‐450.