Acoustic cavitation plays an important role in a broad range of biomedical, chemical and engineering applications, because of its magnificent mechanical and chemical effects. Particularly, the irradiation of the multi-frequency acoustic wave could be favouritely employed to promote these effects, such as enhancing the intensity of sonoluminescence, increasing the efficiency of sonochemical reaction, and improving the accuracy of ultrasound imaging and tissue ablation. Therefore, a thorough understanding of the bubble dynamics under the multi-frequency acoustic irradiation is essential for promoting these effects in the practical applications. The objective of this PhD programme is to investigate the bubble dynamics under dual-frequency excitation systematically with respect to bubble oscillations, the acoustical scattering cross section and the secondary Bjerknes force (a mutual interaction force between two oscillating bubbles). Spherical gas bubbles in water are considered. Both analytical analysis based on perturbation method and numerical simulations have been performed in this thesis. The analytical solutions of the acoustical scattering cross section and the secondary Bjerknes force under dual-frequency excitation have been obtained and validated. The value of the secondary Bjerknes force can be considered as the linear combination of the forces derived under the single-frequency approaches. The predictions of those analytical solutions will be impaired for the cases with large acoustic pressure amplitudes. The numerical simulations reveal some unique features of the bubble dynamics under dual-frequency excitation, e.g., the combination resonances (i.e., their corresponding frequencies corresponding to the linear combinations of the two component frequencies) and the simultaneous resonances (i.e., the simultaneous occurrence of two resonances in certain conditions). The influence of a number of paramount parameters (e.g., the pressure amplitude, the equilibrium bubble radii, the power allocation between the component waves, the phase difference and the driving frequency) on the bubble dynamics under dual-frequency excitation is also investigated with demonstrating examples. Based on that, the parameters for optimizing the dual-frequency approach are proposed. In addition, the effects of thermal effects and mass transfer on the bubble dynamics have also been discussed.