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Abstract: The phenomenon of stochastic resonance (SR) in an asymmetric bistable system driven by correlated multiplicative and additive noise and two periodic fields is investigated. Analytic expressions of the signal-to-noise ratio (SNR) for fundamental and higher harmonics are derived using the two-state theory. The SR appears in both fundamental and higher harmonics. Moreover, the suppression exists for higher harmonics. The effects of static asymmetry and the noise intensity and the strength of coupling between noises on the SNR are studied.