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