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Theoretical studies of the dynamics of a nonlinear oscillator with cubic and quadratic nonlinearities simultaneously excited by low- and high-frequency external forcing are presented. A new mechanism of the appearance of bistability and hysteresis due to such an interaction is discovered. This mechanism manifests as the bistability and hysteresis of tori formed in the oscillator phase space. A comparative analysis of the oscillator behavior under the resonant harmonic excitation and under the dual frequency excitation is made.