The study of the cyclical nature of economic development became a subject of scientific interest in the 19th century. History has proved that the progressive movement of any economic system is not linearly. Periods of intensive growth are replaced by deep crisis phenomena. It was the severe global crises of the 21st century that forced us to pay attention to the topic of cyclicity again and consider the specifics of this issue in various economic sectors, in particular, in tourism. Studies of oscillatory processes in tourism contribute to the prediction of tourist activity, which is of great importance for the practice of tourism regulating, especially during a cyclic crisis. The uneven development of tourism is manifested at all levels: global, regional, local. In some countries, international tourism is developing faster, in others – slower, subject to the influence of both external and internal factors. This pronounced spatio-temporal organization of cyclical fluctuations of international tourism is of particular interest. However, the time series decomposition of inbound tourist flows by individual countries shows significantly different results both on the basis of the manifestation clarity and by the magnitude of the cyclical fluctuations. The purpose of this work is to investigate mathematically justified manifestations of cyclicity in the field of tourism on the example of a number of countries around the world.