This paper studies the theory of gyroresonant interactions of energetic trapped electrons and protons in the Earth's radiation zones with ducted electromagnetic cyclotron waves. Substorm injected electrons in the mid-latitude regions interact with coherent VLF signals, such as whistler mode waves. Energetic protons may interact with narrow-band hydromagnetic (Alfv¿n) waves. A set of equations is derived based on the Fokker-Planck theory of pitch angle diffusion. They describe the evolution in time of the number of particles in the flux tube and the energy density of waves, for the interaction of Alfv¿n waves with protons and of whistler waves with electrons. The coupling coefficients are obtained based on a quasi-linear analysis after averaging over the particle bounce motion. It is found that the equilibrium solutions for particle fluxes and wave amplitudes are stable under small local perturbations. The reflection of the waves in the ionosphere is discussed. To efficiently dump the energetic particles from the radiation belts, the reflection coefficient must be very close to unity so waves amplitudes can grow to high values. Then, the precipitating particle fluxes may act as a positive feedback to raise the height integrated conductivity of the ionosphere which in turn, enhances the reflection of the waves. In addition, by heating the foot of the flux tube with high intensity, RF energy the mirroring properties of the ionosphere are also enhanced. The stability analysis around the equilibrium solutions for precipitating particle fluxes and wave intensity show that an actively excited ionosphere can cause the development of explosive instabilities. ¿ American Geophysical Union 1989