The purpose of this chapter is twofold: to assess the relationship of the nonlinear dynamics of pension systems and economic cycles, and to develop a descriptive evolutionary model of the stages of pension systems. Hodrick-Prescott filter is used to identify cycles in the pension and economic dynamics. The study proved empirically that the evolutionary dynamics of pension systems depends on the cyclicity of national and world economies. In addition, the bifurcation points associate with big Kondratiev cycles, and the fluctuations of the indicators of pension systems correlate with the medium-term Juglar cycles. The crisis starts pension reforms. The results of this study indicate that public pension spending growth is a countercyclical and coincident indicator relative to the global business cycle in 13 countries from 21 of the OECD countries studied. The amount and volatility of public pension spending depends on the basic pension model and has higher values in Bismarck-model countries.