The charcicteriutic features of the instability development in a JInxwelliiln beam-plaenia sys. ten1 with onc previously cscited standing wave is investigated numerically. The unconformity of the simulation results with those predicted by the Single Wave Model is analysed in a smallcold-beam limit..

A comparison is made between the analytical approximations for the maximum growth rate ymas and the corresponding values of the frequency and wave number, which are used as initial conditions in nonlinear theories and numerical experimenb, and the results of an exact numerical solution of the Landau dispersion equation.

The relaxation of the beam-plasma system with several preliminarily ercited unstable waves in its spectrum is investigated on the basis of computer simulations. The nature of the waves and particles interaction during the instnbility development is analysed. It is shown that the destroying of the nmplitude oscillations of the single wave after saturation in the presence of additional waves is caused by tho well known effect of resonance overlapping. A chaotization of the motion of the beam pnrticles occurs even in the case when the amplitudes of the neighbouring waves are small.