  We present a study of the escape time from a metastable state in the presence
of colored noise, generated by Ornstein-Uhlenbeck process. We analyze the role
of the correlated noise and of unstable initial conditions of an overdamped
Brownian particle on the enhancement of the average escape time as a function
of the noise intensity. We observe the noise enhanced stability (NES) effect
for all the initial unstable states and for all values of the correlation time
$\tau_c$ investigated. We can distinguish two dynamical regimes characterized
by: (a) a weak correlated noise and (b) a strong correlated noise, depending on
the value of $\tau_c$ with respect to the relaxation time. With increasing
$\tau_c$ we find : (i) a shift of the maximum of the average escape time
towards higher values of noise intensity and an enhancement of the value of
this maximum; (ii) a broadening of the NES region, which becomes very large in
the strong colored noise regime; (iii) in this regime (b), the absence of the
peculiar initial condition $x_c$ which separates the set of the initial
unstable states lying into the divergency region from those which give only a
nonmonotonic behavior of the average escape time.
