The long-run oil gas price relationship has been challenged more often in recent years, as these two prices have shown evidence of decoupling from each other. This paper proposes the use of a long-memory approach and a rolling-windows method to model the time-varying oil gas price relationship in three markets, namely, the United States, Europe and Japan. The results extend existing research conclusions on the oil gas price relationship and answer the question of whether it is a temporary phenomenon or a permanent market change. Our findings indicate that the US oil gas relationship remains nonstationary at almost all windows and illustrate strong evidence of decoupling. Conversely, the European and Asian oil gas prices exhibit temporary decoupling over time, although the overall relationship still favours the oil-indexation hypothesis. The US experience suggests that oil and gas do not share the same fundamentals and a pricing hub can better reflect the true value of natural gas. Policy makers in Europe and Asia should reinforce their efforts towards a market based pricing mechanism for gas.