  In this article we study the possibility that, due to non-linear couplings,
unstable g-modes associated to convective motions excite stable oscillating
g-modes. This problem is of particular interest, since gravitational waves
emitted by a newly born proto-neutron star pulsating in its stable g-modes
would be in the bandwidth of VIRGO and LIGO. Our results indicate that
nonlinear saturation of unstable modes occurs at relatively low amplitudes, and
therefore, even if there exists a coupling between stable and unstable modes,
it does not seem to be sufficiently effective to explain, alone, the excitation
of the oscillating g-modes found in hydrodynamical simulations.
