<p>Nonstationary waves account for the movement of wave disturbances, with finite periods, whereas the theory of traditional stationary waves has limitations in this regard. Therefore, this study introduces the theory of nonstationary horizontally planetary waves to provide an explanation for the low-frequency characteristics of the global atmosphere. This study theoretically derives the supremum and infimum of phase speed and period of the propagating solutions for nonstationary waves. Both phase speed and period supremum and infimum are determined by the background velocity field, while the period’s supremum and infimum are also related to the zonal wavenumber of the waves. The contributions of meridional and zonal flows to the wave solutions are different. In the upper troposphere, westward-propagating nonstationary waves are primarily located in tropical and high-latitude regions. During the December−January−February (DJF) and March−April−May (MAM), eastward-propagating of nonstationary waves occurs in the tropical westerly duct region. Over the eastern Pacific, the periods of these waves are greater than 60–80 days or less than 20–40 days, while over the Atlantic, they are greater than 60 days or less than 50 days. In the lower troposphere, during DJF and MAM, nonstationary waves in the tropical region (60–150°&#xa0;E) exhibit eastward propagation, corresponding to the Madden-Julian Oscillation (MJO) signal. In most tropical regions, westward-propagating nonstationary waves dominate on intraseasonal timescale. In mid-latitude regions, eastward-propagating intraseasonal oscillation (ISO) signals are observed, while in monsoon regions, the period characteristics reflect the features of monsoon ISO.</p>