Abstract: This paper is devoted to research and identification of medium- and long-term economic cycles. The study of the peculiarities of cyclical economic development by using statistical approaches is one of the necessary components for the countercyclical regulation of the economy at the macro and meso levels. One of the problems of studying economic cycles, in particular long-term ones, is the choice of an adequate method by using which it is possible to identify and explain the nature of the economic cycle according to available statistical data. This is the basis for forecasting future economic dynamics. In addition, the questions of determining the duration of the cycles of Juglar, Kuznets, Kondratieff remain unresolved. For this purpose the paper conducted a spectral analysis of time series of GDP per capita for England, the United States and France for the period from 1820 to 2016. To ensure stationarity, we converted the original time series into growth rates (year to previous year). In addition, all time series were smoothed by a moving average of the 5th order. The use of moving averages of different orders allows to get rid of high-frequency noise. As a result of the spectral analysis, the charts of the periodogram and the spectrogram for England, the USA and France were received, which are the basis for identifying and evaluating the period of economic cycles. The well-known results for all three countries are the most clearly identifiable medium-term economic cycles. At the same time, for the European countries (England and France), Juglar’s cycles (9-14 years) were the most significant, and for the USA — Kuznets’ cycles (18-28 years). For the long waves (38-55 years), the harmonics have a lower amplitude in the spectral decomposition (especially for the USA), which does not allow clear to identify them.