This article tests four hypotheses about gender differences related to membership in voluntary pension systems in Eastern European countries that belong to different groups "aging, early reformers" (Romania) and "aging, late reformers" (Ukraine). In order to test the hypotheses, we consistently applied three methods to time series of participants' growth rates in the Pillar III of Romanian and Ukraine pension systems: cyclical analysis of time series using the Hodrick-Prescott filter, fractal analysis by conducting Rescaled Range Analysis (R/S-analysis) of time series, and phase analysis of time series. All three methods have confirmed the hypothesis that the parameters of nonlinear behavior depend on gender. R/S-analysis showed that the behavior of men and women in both countries is antipersistent behavior with short-term memory, but the gender gap in Hurst exponent estimates is greater in Romania than in Ukraine. Using fractal and phase analysis, we confirmed the hypothesis that gender differences in behavior patterns increase as financial and stock markets develop, as the gender gap in financial knowledge increases. However, at given the level of significance, the hypothesis that economic fluctuations affect behavior patterns, and the level of influence depends on gender has not been confirmed.