The work is dedicated to the study of the stability problem of the system “fast electron beam – gas-discharge plasma” (EBPS) under conditions typical for electron beam - pumped lasers. In some cases, the commonly used hydrodynamic approach is not applicable and kinetic consideration is required. Based on this approach, the stability of the EBPS is investigated under conditions when pumping the active media of high–power gas lasers, the electron beam energy being significantly higher than the average energy of the resulting plasma electrons. The beam density, on the contrary, is significantly less than the plasma density. When developing the theory, both plasma and beam noises were considered. It is shown that under the conditions in question, the main role is played by the beam noise, which is transferred to the EBPS due to a shift with a velocity of the order of the velocity of the beam electrons.