Preliminary results concerning the fine vertical structure of the stratospheric flow in the middle stratosphere, above 18 km, are presented. By using a high-resolution anemometer hung below slowly rising and descending balloons, the wind shear vector was measured over vertical distances as small as 50 m. Most of the soundings reveal an organized structure with a vertical wavelength of about 1 km. Shear instabilities are generally related to these structures. These observations, more detailed than those obtainable using radar-balloon methods, suggest that long-period inertio-gravity waves are responsible for much of the variability.