A very general approach to hydromagnetic instability in a magnetospheric geometry is given. The specific effects of the presence of finite &bgr; ring current particles and cold particles of ionospheric origin are included. The generality of approach allows the theory to interrelate various approaches to low-frequency stability. It is concluded that resonant particle instabilities are likely to be the source of low-frequency oscillations that have been observed. Instability conditions and growth rates are estimated. Alfv¿n waves may be excited with &bgr;1, compressional disturbances are expected to be generated.