  We present a study of the escape time from a metastable state of an
overdamped Brownian particle, in the presence of colored noise generated by
Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the
enhancement of the mean first passage time through a potential barrier and on
the behavior of the mean growth rate coefficient as a function of the noise
intensity. We observe the noise enhanced stability effect for all the initial
unstable states used, and for all values of the correlation time $\tau_c$
investigated. We can distinguish two dynamical regimes characterized by weak
and strong correlated noise respectively, depending on the value of $\tau_c$
with respect to the relaxation time of the system.
