We study the influence of nonlinear circularly polarized waves, propagating backward relative to the external magnetic field, on the behavior of linear instabilities in a system composed of electrons, background protons, and a proton beam. We find that the presence of both nonlinear left- and right-handed polarized backward-propagating waves induces the stabilization of linear right-hand polarized forward-propagating instabilities when the amplitude wave is above a threshold value. It is shown that the threshold amplitude is lower for backward-propagating waves than for forward-propagating waves in the parameter space we surveyed. We also find that the presence of nonlinear backward-propagating waves can destabilize linear ion-acoustic modes. These ion-acoustic modes are supported either by the proton core or by the proton beam. The instabilities occur when the phase velocities of the forward- and backward-propagating ion-acoustic waves relative to the proton core or to the proton beam become equal. We study the dependence of the amplitude threshold on the large-amplitude wave frequency, the plasma-β of the various species, and the proton-beam velocity. These results have already been invoked in order to explain some features of the solar wind. We believe that they can also be important in the study of other stars and quite generally in any astrophysical system involving beam-plasma interactions.