We present measurements of oscillations in the electron density, ion density and ion velocity in the induced magnetosphere of Mars. The fundamental frequency of the oscillations is a few millihertz, but higher harmonics are present in the spectrum. The oscillations are observed in a region where there is a velocity shear in the plasma flow. The fundamental frequency is in agreement with computational results from an ideal-MHD model. An interpretation based on velocity-shear instabilities is described.