[en] In a standard pulsar model, the radio emission is produced in the relativistic, strongly magnetized electron-positron plasma in the polar-cap region of the magnetosphere. Waves are generated well below the cyclotron frequency and must propagate through the cyclotron resonance region where they are affected by the resonance. Wave dispersion near the cyclotron resonance is discussed in the formalism of the weak anisotropy approximation in which the relevant waves are treated as transverse. Analytical approximations for the two orthogonal modes are derived, in the rest frame of the plasma, for nearly parallel, nearly antiparallel and nearly perpendicular propagation with respect to the magnetic field direction. It is shown that due to the relativistic distribution the wave dispersion varies smoothly across the resonance with initially elliptical polarization evolving to linear and then elliptical polarization with opposite handedness. The relevance of such a change in handedness to the interpretation of circular polarization is discussed