This study mainly explores the effect of market states (price and returns) on the relationship between spot and futures oil prices and targets three important issues: long-run cointegration, causalities, and market efficiency. Based on previous studies exhibiting bi-directional causality between spot and futures oil prices, this study employs quantile regressions to examine the possible feedback effect in their long-run cointegration and their causalities. In particular, it allows for exploring the possible asymmetric responses between spot and futures markets. The empirical results herein find that the long-run cointegrated relationship between contemporaneous spot and futures prices is impacted by the states of the spot markets. Similarly, whether futures oil prices lead spot oil prices is relevant with the states of the futures markets. This study also examines the efficiency of crude oil markets and shows that the efficiency is related to the length of futures contracts. These findings offer some implicative suggestions and strategies.