The propagation of one and two electron beams in a plasma is considered in the case when the source is time-dependent. When the electron-plasmon interaction time is assumed to be much less than the electron flying-off time, the main gasdynamic equations are obtained on the basis of the quasilinear theory of weak turbulence. The solution for a monoenergetic beam is a beam–plasma structure moving with constant velocity. In general, two beams propagate as two beam–plasma structures with constant velocities. However, the second electron beam influences the flying-off dynamics of both beams. This peculiar interaction modifies the shapes of the structures.