  In this paper we study the effects of rotation on the frequencies of the
quasi-normal modes of a proto-neutron star (PNS) born in a gravitational
collapse during the first minute of life. Our analysis starts a few tenths of
seconds after the PNS formation, when the stellar evolution can be described by
a sequence of equilibrium configurations. We use the evolutionary models
developed by Pons et al. (1999; 2001) that describe how a non rotating star
cools down and contracts while neutrino diffusion and thermalization processes
dominate the stellar dynamics. For assigned values of the evolution time, we
set the star into slow rotation and integrate the equations of stellar
perturbations in the Cowling approximation, both in the time domain and in the
frequency domain, to find the quasi-normal mode frequencies. We study the
secular instability of the g-modes, that are present in the oscillation
spectrum due to the intense entropy and composition gradients that develop in
the stellar interior, and we provide an estimate of the growth time of the
unstable modes based on a post-Newtonian formula.
