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The purpose of the study is to identify cyclical fluctuations by means of two methods used to determine the cyclical nature of various phenomena. The first approach is based on the modified Harvard method. The other approach uses the Hodrick-Prescott filter and the Baxter-King filter. Cyclical fluctuations are observed not only in series of economic variables, but also in the case of demographic variables. The cyclicity of demographic data has been investigated by the author previously, and so time series for the number of births in Poland and Sweden were used for the study. The conducted analysis of the time series indicated that the number of births is subject to cyclical fluctuations and enabled their principal morphological properties to be established, i.e., the periods in which turning points occur, the fluctuation cycle periods, their lengths and amplitudes.