Plasmas at high-electron temperatures can carry transverse waves in which self-magnetic fields and relativistic effects become important. The relativistic perturbation equations for an isotropic uniform plasma are solved as an initial-value problem, i.e., by Laplace transformation and the propagation or dispersal of both longitudinal and transverse perturbations is calculated. In both cases transients occur which have a continuous frequency spectrum. While transverse perturbations also yield pure persistent waves (with phase velocity exceeding that of light) of all wavelengths, longitudinal perturbations of very shont wavelength will not he propagated as pure waves but will die out eventually with only longer wavelengths persisting. The transverse plasma perturbations discussed are nonvortical and the dispersal of vortices is covered by a separate discussion. The vortices do not give rise to a new mode of propagation of perturbations. (auth)