In this paper, time-varying co-movements between the stock markets of Poland, the Czech Republic, Hungary, and the capital markets of developed countries in stable and crisis periods are studied. The parameters of the VAR-AGDCC-GARCH (Vector Autoregressive- Asymmetric Generalized Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroscedasticity) model are estimated, and volatility spillovers are calculated. The evidence suggests that the level of correlation between stock return shocks of Central and Eastern European countries increased significantly in the period of financial turmoil and was high in the period of the US sub-prime crisis, as well as during the euro area sovereign debt crisis. After the announcement of the OMT (Outright Monetary Transactions) program, the evolution of the stock market indices in Central and Eastern Europe countries (CEECs) have followed different paths. An analysis of the volatility spillovers indicates that CEECs are the recipients of volatility. In the period of 2004–2019, they received much volatility—from Germany and the US, in particular. They also received much volatility from Spain during the euro area sovereign debt crisis. After 2012, volatility transmission to Poland, the Czech Republic, and Hungary dropped significantly.