Abstract: The relation between wind direction fluctuations and the structure of the stable atmospheric boundary layer are described. Using data from the sonic anemometers on the atmospheric observatory tower in Boulder, Colorado, the variations of the vertical and lateral wind direction fluctuations with averaging lime are calculated. The results indicate that variations of σw/U and σv/U with averaging time are correlated with the vertical and lateral energy spectra. The peaks in the curves of σw/U and σv/U with averaging time correspond to the time scales of the peaks in the energy spectra. The wind shear usually appear with internal gravity wave. The functional dependence with height and Ri of the wind direction parameters are described for the simplest ground-based inversion case with only limited success. The more complicated stable layers can not be properly described with simple empirical functions.