Electromagnetic waves and charged particles in the magnetosphere may exchange energy through the cyclotron resonance interaction. If the nonthermal particles have an anisotropic pitch angle distribution, VLF and ULF signals may be amplified over well-defined broad bands of frequencies. An analytic solution of the dispersion equation is obtained for a particular anisotropic distribution which simulates magnetospheric conditions, and the instability is found to be unique and convective. Frequency spectra of the net power transfer along whistler paths are presented for a class of distributions which are thought to be typical of quiescent conditions in the magnetosphere. Finally, the theory is applied to experimental amplitude measurements of a VLF whistler event to illustrate its potential for estimating the phase space distribution of nonthermal particles in the magnetosphere. (Author).