This study investigates both the constant and time-varying conditional dependency between crude oil and stock markets for the CEE countries (Hungary, Poland, Czech Republic, Romania, and Croatia) by using the conditional copula-GARCH model with both constant and time-varying dependence parameters in the field of energy economics. Through different copula functions, the proposed models allow specifying the joint distribution of the crude oil and CEE stock returns with full flexibility. First, from the copula models, we find that all series show fat-tail, leverage effects, and volatilities tend to cluster. Second, in both constant and timevarying copula models, we find that conditional dependence is similar for most countries, which means that a significant conditional dependence exists in all oilstock price pairs. Our findings have important implications for both policymakers and investors by contributing to a better understanding of oil-stock relationships. A significant interdependence between crue oil price and stock markets suggests that enterprises and governments in CEE regions should pay attention to the stock market performance when the oil price fluctuates.