- The properties of low-frequency waves in a one-dimensional, relativistic electron-positron plasma in a strong external magnetic field typical of pulsar magnetospheres are discussed. Approximate dispersion relations are derived for a broad class of distribution functions that have an intrinsically relativistic spread in energies. The effects of the non-neutrality, associated with rotation, and of the relative motion of the plasma species are discussed briefly. In the plasma rest frame only three wave modes need be considered. The magnetosonic (t) mode becomes firehose unstable as the magnetic field weakens, and this occurs in the wind zone of the pulsar. The Alfvén (A) mode exists only below a maximum frequency, and is weakly damped only for sufficiently strong magnetic fields. The Langmuir-O mode is approximately longitudinal near its cutoff frequency, and approximately transverse at high frequencies. We argue that the emission zone is within ∼102 pulsar radii, and that only t, A, and Langmuir waves may participate in the formation of the observed radio spectrum.