Abstract: The phenomenon of stochastic resonance (SR) andphase-synchronization between the input signal and the output signal in abistable system were investigated. At first, we obtained the expressions ofthe output signal-to-noise ratio (SNR) and the averagephase-synchronization time between the input signal and the output signal,and then the relationship between SR and the averagephase-synchronization time was studied. The results show that: (1) SRappears, and the average phase-synchronization time is sensitive tonoise. For the simultaneous existence of the multiplicative noise andadditive noise, there is a restraint, and then a peak in the curve of theoutput SNR and the average phase-synchronization time with theincrease of additive noise intensity. Moreover, the decrease of the ratio ofmultiplicative noise intensity and additive noise intensity can increase theoutput SNR and the average phase-synchronization time. (2) SR andthe maximum of the average phase-synchronization time appear atdifferent times, but the average phase-synchronization time issensitive to the output SNR. These results may be helpful in signalprocessing where the working environment can be tuned according to theprinciple of SR.