Liquid sloshing in square or nearly square-base tanks becomes more complex due to the emergence of three dimensional waves around resonance. Because of symmetrical base in a square tank, two predominant sloshing modes (along the plane of excitation and orthogonal to the excitation plane), simultaneously emerge even if the tank is resonantly excited in one direction. For relatively small liquid-depth, nonlinear effects shift the resonant sloshing frequency. So, the effectiveness of devices (Tuned Liquid Dampers) designed based on the linear theory will be affected. The present study investigates the existence of the sloshing wave systems and their frequency bounds with an extensive experimental data. The tank is subjected to horizontal harmonic excitation for a wide range of frequencies and amplitudes. Sloshing induces different wave systems which depend on excitation frequency, excitation amplitude and liquid-depth. The main focus is to determine the frequency bound of swirling waves for a range of excitation amplitudes and liquid-depths. It has been found that the frequency bound of swirling increases with excitation amplitude. © 2020 Elsevier Ltd