[en] The one-dimensional problem of exciting stationary nonlinear oscillations of finite amplitude in cold collisionless plasma by a finite electron beam, is considered. The dependence of the characteristics of longitudinal nonlinear oscillations on the beam parameters is studied. The connection between the longitudinal and transverse oscillations results in the solutions of the equation for velocity components being unstable due to the terms proportional to β²(β11) for the transverse components in the equations. Under application of an external magnetic field the instability of the solution is not removed, though its character changes