Temporal behavior of some physical quantities is investigated for the system of electron plasma and injected beam with fixed velocity distributions. The fluctuation of the electric field with the critical wavenumberk0(defined by&ggr;ko = 0) grows secularly; the velocity diffusion coefficient forv0(defined by&ohgr;ko = k0·v0) grows in proportion to logt; the rate of energy loss by the beam approaches the enhanced value ast−1/2.