We examine the quantile serial dependence in crude oil prices based on the Linton and Whang’s quantile-based portmanteau test which we improved by means of quantile wild bootstrapping (QWB). Through Monte Carlo simulation, we find that the quantile wild bootstrap-based portmanteau test performs better than the bound testing procedure suggested by Linton and Whang. We apply the improved test to examine the efficiency of two crude oil markets – WTI and Brent. We also examine if the dependence is stable via rolling sample tests. Our results show that both WTI and Brent are serially dependent in all, except the median quantiles. These findings suggest that it may be misleading to examine the efficiency of crude oil markets in terms of mean (or median) returns only. These crude oil markets are relatively more serially dependent in non-median ranges.