Characteristics of waves in a two-com ponent co ld plas ma are reviewed. Using the ClemmowMullaly-Allis diagram, th e topolo gical types of the wave-normal surfaces are shown. A co nsiste nt system of labelin g the mod es, initially gi ve n by Alli s, is exp lained. Reversal in the polarization in th e electric field is examined, and all th e mod es in whi c h the re versal occurs are specifi ed. Th ere is no polarization re versa l in ULF to VLF waves in the magnetos phe re. The lower hybrid resonance frequen cy in the magne tosp he re is discussed.The equations of motion for an elec tromagn eti c ray a re derived. Defi ning the action for the ray with analogy to that for a parti cle in c lass ical mec hani cs, the principle of least action is proved. It is s hown th at if the dispersion relation is hom oge neo us in th e wave vec tor and the freque ncy, th e princ iple of leas t action impli es the principle of least tim e, i.e., Fermat's prin cipl e. When th e principle of least time hold s, as is the case with Alfven co mpressional waves, th e trajec tory of 'a ray can be determined from a variational eq uation , from which th e probl e m can be formulat ed in Hamiltonian form. For th e axially sy mm etric case, th e generali zed mom e ntum co njugate to th e azimutha l coordinate is a constant of moti on. Us in g thi s relation, "al lo wed" a nd "forbidden" region s are defin ed wh e n a set of initi al co ndition s for th e ray is give n. This me thod is app li ed to a mod el magne tosp here with a dipole magne ti c field. It is show n that the accessibility of hydro magnet ic rays originating from the boundary of th e ma gne tosphe re to th e earth is great ly limited. For a distorted magne tosp he re the canonical eq uations for a hydromagne ti c ray are int egrated by a num eri cal me thod. Typi ca l traj ec tories in the equatorial plane are shown, and th e effects of the deformation of th e dipole fi eld on the ray traj ectories are discussed.