This paper investigates the uncertainty-dependent and sign-dependent effects of the oil market fundamental shocks, namely supply, aggregate demand and oil-specific demand shocks. We do so by first proposing a novel oil uncertainty index that is measured by the stochastic volatility of the unpredictable component of oil prices. We then employ a nonlinear model and find that the all reactions of oil production, real price of oil, and global economic activity to the structural shocks are regime-dependent. Moreover, we extend the model to accommodate positive and negative oil market shocks to examine the possible asymmetric effects. In relation to real economic activity, the effects of oil supply shocks are asymmetric regardless of the state of the market, but oil-specific demand shocks are only asymmetric when oil price uncertainty is high.