Electrostatic oscillations in a stationary beam double layer are studied in the hydrodynamic approximation. An analysis of the solutions to the linearized equations for perturbations shows that the double layer in an unbounded plasma may be subject only to convective instability, in which case the perturbations localized inside the region of the potential jump escape from the plasma without distorting the steady field structure. The double layer in a bounded plasma is investigated numerically by a particle-in-cell method. It is established that, as is the case in the Pierce system, the governing role in the stability of the double layer is played by the field of the charges induced on the surfaces of the conducting electrodes. © 2002 MAIK "Nauka/Interperiodica".