The interrelationship between the oscillation amplitude and the form of the energy distribution function of beam electrons is studied under conditions where the electron beam predominantly excites longitudinal plasma oscillations. It is shown that the intensity of the oscillations stops growing when the distribution function assumes the form of a plateau extending to thermal velocities of the plasma electrons. Experimental measurements of the beam relaxation distance as a function of the parameters of the plasma-beam instability are in qualitative agreement with theory.Initial modulation of an electron beam by means of a monochromatic signal of sufficiently high amplitude, leading to a considerable narrowing of the oscillation spectrum, reduces the relaxation distances and the number of anomalously fast electrons in the beam.