A high-&bgr; model for the generation of ultralow-frequency (ULF) fluctuations at the magnetopause is presented. The ULF waves are excited by the density gradients in the magnetopause boundary layer. For &bgr; varying between 0.1 and 1.0, and for realistic values of the density gradients, the frequency range of the excited modes, their transverse wavelengths and their phase velocities parallel and perpendicular to the geomagnetic field lines seem to be in agreement with recent observations of Alfv¿nic structures at the magnetopause. ¿ American Geophysical Union 1993