The effects of the correlation time τ between noises on the noise-enhanced stability （NES） phe- nomenon in an asymmetric bistable system driven by cross-correlated noise are investigated. The ex- pressions for the average escape time from the left metastable state TL and from the right metastable state TR are derived. The results indicate that： i） The NES effect is suppressed as the correlation time τ increases for two metastable states; ii） The increase in τ speeds up the escape process from the right state for positively correlated noise, whereas its role is reverses for negatively correlated; iii） In the escape process from the left state, the role of τ is opposite to that in escape from the right state.
