The transient properties of a bistable system driven by cross-correlated no
ises are investigated; the correlation times of the correlations between th
e noises are nonzero. The mean first-passage time (MFPT) is calculated. Fro
m numerical computations we find the following: (1) The MFPT of the system
is affected by both the correlation time tau and the correlation strength l
ambda; (2) tau and lambda play opposing roles in the MFPT; (3) when lambda
or alpha/D(alpha and D are the additive and multiplicative noise intensitie
s respectively) are far away from 1, the MFPT as a function of tau is monot
onic; however, when both alpha/D and lambda approach 1, the MFPT as a funct
ion of tau is nonmonotonic; (4) for the case of perfectly correlated noises
(lambda=1), the MFPT corresponding to alpha>D and alpha<D exhibit the same
behaviors and the MFPT for alpha=D is continuous, which is very different
from the case of the tau=0 [Phys Rev. E 53, 5764 (1996)].