This paper studies co-movements between world oil prices and global prices for corn, soybean and wheat using copulas. Several copula models with different conditional dependence structures and time-varying dependence parameters were considered. Empirical results for weekly data from January 1998 to April 2011 showed weak oil-food dependence and no extreme market dependence between oil and food prices. These results support the neutrality of agricultural commodity markets to the effects of changes in oil prices and non-contagion between the crude oil and agricultural markets. However, dependence increased significantly in the last three years of the sampling period, even though upper tail dependence remained insignificant, indicating that food price spikes are not caused by positive extreme oil price changes. These results have implications for policy design, risk management and hedging strategies. (C) 2012 Elsevier Ltd. All rights reserved.