The theory of low-frequency (compared to ion cyclotron) arbitrary-&bgr; modes is developed for the following system: a two-component (hot and cold) inhomogeneous plasma, and a straight inhomogeneous magnetic field. This system is taken to model the magnetosphere, near the geomagnetic equator. The stability properties of three modes are presented in detail: the drift-compressional mode (driven by pressure gradients) the firehose mode (driven by T∥>T⊥), and the drift mirror mode (driven by T⊥>T∥). Comparisons to earlier models and to one observed event are also presented.