Analytical expressions for the components of the dielectric permeability operator tensor of plasmas confined in planetary dipolar magnetospheres are derived. The kinetic Vlasov's equation of a two-dimensional plasma model, confined by an axisymmetric mirror trap, with circular magnetic field lines has been used. The conditions for single-particle resonances of trapped particles are discussed, taking into account the bounce resonances. It is shown that the collisionless Cherenkov damping of the Alfv¿n and magnetosonic waves differs substantially from the Cherenkov damping of these modes in the straight confining magnetic field case; this is true due to the presence of the trapped particles. Estimations of the damping coefficients for Langmuir and kinetic Alfv¿n waves are made, and some observational consequences of this study are discussed. ¿ American Geophysical Union 1996