Investigation has been made of the effect of thermal plasma electron and ion motion on wave propagation in a non-relativistic, low-pressure plasma across a magnetic field. The dispersion equation for an ordinary wave has the solutions ωs(k) close to sωα (s = 1, 2...) for any ratio of wavelength (ƛ = 1/k) to the Larmor radius ϱα of the α type particles having thermal velocity (see fig. 1)). In order of magnitude ωs(k)−sωα≈−xαωα for kϱα≈1.The dispersion equation for an extraordinary wave has also an analogous solution (see fig. 5) in the high-frequency region (ω ≈ ωe), and also a solution corresponding to longitudinal plasma oscillations for k2ϱα2 ≫ xα Longitudinal-oscillation frequencies for the case of a dense plasma, when Ωe ≫ ωe (Ωe is the electron Langmuir frequency, and Ωe their gyro-frequency) decrease for an increase of kϱe, diminishing from the values ω ≈ sωe (s = 2, 3...) for kϱe ≪ 1, down to ω ≈(s − l)ωe for kϱe ≫ 1 (see fig. 5). For a low-density plasma (Ωe ⪅ ωe), plasma-frequency behaviour is shown in figs. 2 and 3.In the low-frequency region (ω ⪅ ωi) the dispersio equation for an extraordinary wave determines (for the case of a cold plasma) the frequency ω = kFA corresponding to a magneto-acoustic wave (VA is the Alfvén velocity). This expression is inapplicable for kϱ1≈s(s = 1, 2...) when ω≈sωi. In this region it is necessary to take into account thermal ion motion. Behaviour of the various branch frequencies of an extraordinary hot-plasma wave for ω ≈ ωi fin coi is comparatively complex (see fig. 6).Investigation has been carried out of the self-excitation (caused by beam instability) of electron (high frequency) branches of the oscillations discussed, for the passage of an ion cyclotron wave through a plasma.