In this paper, we investigate the degree of persistence of dependence between crude oil prices and stock markets in the Gulf Cooperation Council (GCC) countries in order to verify whether crude oil prices effect on these markets is immediate or delayed. Using daily data over the period 2010–2017 and based on copula functions, empirical results show that the oil-GCC stock markets relationship is significantly positive and show a different degree of persistence. Furthermore, the Saudi market experiences the highest degree of persistence in the dependence with oil prices. Also, we find very strong persistence in the upper tail compared to the lower tail dependence. The empirical evidence also indicates that dependence between oil and the six GCC stock markets increase significantly after the recent oil price collapse of 2014 leading to an increase in the persistence of dependence for the almost of oil-GCC stock markets pairs and allowing for a spillover effect in some countries. Finally, by taking into account the oil prices asymmetry, we find that generally, the oil price does not affect the persistence of dependence. Our findings allow for a reliable and efficient stock indexes forecasting and portfolios design framework for risk managers and investors based on facts in the oil market.