The problem of Landau damping in plasma oscillations is studied in a relativistic gas and the asymptotic forms of the dispersion relation and the damping coefficient are obtained in the non‐relativistic as well as in the relativistic limits. In the relativistic limit it is found that while the damping is very strong in the case where the phase velocity is small compared to the velocity of light, it is absent when the phase velocity exceeds the velocity of light. Moreover, in the former case, in the extreme relativistic limit the damping becomes independent of the plasma temperature.