  We study the gravitational radiation associated to the non--radial
oscillations of newly born, hot neutron stars. The frequencies and damping
times of the relevant quasi--normal modes are computed for two different models
of proto--neutron stars, at different times of evolution, from its birth until
it settles down as a cold neutron star. We find that the oscillation properties
of proto--neutron stars are remarkably different from those of their cold, old
descendants and that this affects the characteristic features of the
gravitational signal emitted during the post-collapse evolution. The
consequences on the observability of these signals by resonant--mass and
interferometric detectors are analyzed. We find that gravitational waves from
the pulsations of a newborn proto--neutron star in the galaxy could be detected
with a signal to noise ratio of 5 by the first generation interferometers, if
the energy stored in the modes is greater than $\sim 10^{-8} M_\odot c^2$, or
by a resonant antenna if it is greater than $\sim 10^{-4} M_\odot c^2$. In
addition since at early times the frequency of the spacetime modes is much
lower than that of a cold neutron star, they would be also detectable with the
same signal to noise ratio if a comparable amount of energy is radiated into
these modes.
