A relativistic theory of transverse oscillations in hot, magnetized, isotropic equilibrium plasmas is presented. The special theory of relativity enters the description with the requirement that the particle masses depend on the particle velocities which themselves are limited by the speed of light. Using the relativistic Maxwell-Boltzmann-J¿ttner (MBJ) distribution correctly describing the equilibrium state of a plasma, we formulate the dispersion relations for subluminal as well as superluminal waves, using the Trubnikov representation. For Landau damping of transverse wave modes, the so-called cyclotron damping, an analytical expression generalizing earlier results to a relativistically correct form is derived. The theory is applied to an electron-proton plasma, the main constituents of the interplanetary medium. Special consideration is given to the regime of weak damping of low- and high-frequency waves in the interplanetary plasma. The resulting dispersion relations and damping rates are used to determine cosmic ray transport parameters in the interplanetary medium, in particular the mean free path of solar energetic particles and the related modulation parameter of galactic cosmic rays in a simple diffusion-convection modulation model. It is shown that at particle rigidities below about 109 V/c the mean free path and the modulation parameter are significantly different for cosmic ray protons, negatrons, and positrons because of the different handedness of the particles in the ordered interplanetary magnetic field and the different Landau damping rates of right-handed and left-handed circularly polarized plasma waves.¿ 1997 American Geophysical Union