The article deals with business cycles of selected European countries for the long period of time - since 1960. The group of analysed countries is represented by the member states of the Economic and Monetary Union. The analysed group of countries contains both members sharing the single common currency euro and selected countries that decided to keep their national currency. The article examines development of business cycles during a long period of time. This will be done by the Hodrick-Prescott approach to a detrending of time series. Symmetries in business cycles are finally analysed by comparing the business cycles of the EMU member states. Then it is possible to analyse whether there is any core and periphery within the EMU according to the business cycles or not.