In this paper, the global structural relationship between the prices of crude oil and natural gas is investigated using the recently introduced decomposition of the real price of crude oil by Kilian (2009). A four-variable structural vector autoregressive model (SVAR) for oil and natural gas markets is developed for this investigation. We find some evidence that the crude oil market affects the natural gas market through a combination of demand shocks rather than through oil supply shocks. The uncertainty about future oil supply causes precautionary demand in the oil market, which shifts to the natural gas market and increases the natural gas price as the primary substitute for oil. Meanwhile, global demand shocks influence both crude oil and natural gas prices, which leads to similar fluctuations in the prices of oil and natural gas. Consequently, demand shocks link oil and natural gas markets and produce similar changes in their prices