Several time series of vertical wind velocity profiles obtained by tracking spherical superpressure balloons using l1–20 radars at Point Mugu, California and Cape Kennedy, Florida are analyzed. In the altitude range 11–20 km the measured wind data are an order of magnitude better than standard GMD-1 data. Below 11 km the smooth 2-m diameter spherical balloon used is aerodynamically unstable, producing spurious high frequency oscillations. Each series contains from 8 to 18 wind velocity profiles spaced over a period of time from 8–12 hr. Every profile in each series contained mesoscale perturbations of from 5–10 m sec−1 and 5–20 deg (referenced to an arbitrary smooth profile), through depths up to 2 km, which persisted in recognizable form at approximately constant altitude throughout the series. A model to account for such perturbations is presented, picturing the atmosphere from 11–20 km as having a distinctly layered structure. Each layer covers a large horizontal area and contains air whose motion is principally controlled by a quasi-inertial oscillation. Wind profile perturbations result from the relative horizontal motion between layers. It is suggested that, in the presence of geostrophic wind shear, overall thermal stability, and low turbulence energy normally found in the stratosphere, quasi-inertial oscillations, once started through a deep atmospheric layer, would soon disperse into a series of shallow individual ones of different wavelengths, capable of maintaining themselves for long periods of time.