Nonlinear vibrations of elastic structures containing two cylindrical liquid-filled tanks subjected to vertical harmonic excitation are investigated. When a 2:1:1 ratio of internal resonance is satisfied between the natural frequencies of the structure and the sloshing in the two liquid tanks, nonlinear parametric vibrations can be observed. The equation of motion for the structure is derived considering the nonlinearity of the hydrodynamic force, and the modal equations for sloshing are derived by using Galerkin's method. Then, frequency response curves are determined by using van der Pol's method. The respective influences of the liquid levels and the deviation of the internal resonance ratio 2:1:1 on the frequency response curves are discussed. The results of the response curves differed from those obtained in the case where a structure had only one liquid-filled tank installed. It is found that two types of vibrations may occur depending on the excitation frequency and the liquid levels: a single-mode solution (sloshing occurs in either tank) and a double-mode solution (sloshing occurs in both tanks). Amplitude and phase modulated motion appears in the single-mode solution when some deviation of the internal resonance ratio exists. The validity of the theoretical results was verified by the experiments.