Tl1e forced nonlinear Alfven oscillations in a system with a discrete spectrum are considered. In such a system, the discreteness of the spectrum or dissipation may cause stabilization of unstable processes of interaction between the initial Alfven wave and small perturbations. For this case, a correction to the natural frequency of small stationary oscillations has been found. The bifurcation of the oscillation amplitude was shown to occur under changes of the driving force frequency. This effect must be taken into account when describing plasma dynamics in MHD resonators, such as the earth's polar ionosphere and solar coronal loops.
Sternberg State Institute of Astronomy, Moscow State University, Leninskie Gory, Moscow, 119992, Russia