The magnetic fluctuations, at the magnetopause and in the adjacent magnetosheath, exhibit power law spectra which are very reminiscent of turbulent spectra. In prospect of future modelizations of such a turbulence, new information is brought about the experimental properties of these fluctuations. The power laws spectra previously obtained in the ULF range are shown to hold also in VLF, up to the lower hybrid frequency. Concerning the polarization, 1) the direction with respect to the static magnetic field is shown to be dominantly perpendicular at low frequencies, consistently with Shear Alfven modes in this range, and 2) no right-hand sense of rotation can be evidenced at frequencies higher than the proton gyrofrequency, although one could expect the fast magnetosonic mode to be dominant in this range. The physical implications of this last observation for the non linear effects at work in the turbulence are briefly discussed. ¿ 1999 American Geophysical Union