The velocity distribution of the electrons within a plasma shock front is investigated by methods of the kinetic theory arranged in a manner to account for heavy deviations from thermodynamic equilibrium. The distribution function exhibits two peaks and becomes unstable with respect to electron oscillations if the shock wave is sufficiently strong (MACH number M ≳ 6.5). The second peak is formed by run-away-electrons, i. e. those fast electrons which transgress the shock front from the hot region. The frequencies, wave numbers, growing rates, phase and group velocities of the excited oscillations, and the influence of the OHMIC damping are calculated approximatively. The results are applied to the non-thermal radiofrequency radiation of the sun.