A kinetic theory, allowing finite ion Larmor radii, general magnetic field geometries and plasma equilibria, has been developed for hydromagnetic Alfv¿n waves excited within the Earth's magnetosphere by the storm-time energetic ring-current particles. In particular, assuming adiabatically injected particles, it is found that the excitation mechanism is due to the magnetic drift-bounce resonances of highly enegetic protons and the various predicted instability properties are consistent with satellite observations. ¿ American Geophysical Union 1988