A nearly inertial evolution of the relative velocities measured by differential sounding (Barat, 1982a) has been observed along a balloon flight in the 26-30 km altitude range. The vertical structure of the flow appears to be a stack of layers a few hundred meters wide undergoing independent, nearly inertial oscillations added to the mean flow, the transitions between adjacent layers being characterized by abrupt rotations of the horizontal wind. We show that the stability of such a structure, despite the very high wind shears encountered within transitions, is consistent with the very weak turbulent viscosity coefficient independently estimated. As a tentative interpretation of our observations we suggest that they are related to the dissipation of an internal gravity wave near a critical level.