A general expression for the tensor of the dielectrical susceptibility in a
n anisotropic plasma with particle drifts is derived, and the dispersion eq
uation is found for waves propagating in arbitrary direction with respect t
o the mean magnetic field. The dispersion equation is solved for the case o
f electromagnetic ion-cyclotron waves. It is found that in the plasma of th
e auroral magnetosphere strong plasma instability may occur so that the val
ue of the growth rate of the waves is of the order of the wave frequency. B
esides, the plasma instability is excited at less values of the wave number
if the magnetospheric altitude becomes larger.