The aim of this paper is to examine the long run relationship between the world oil price, economic growth demand, and inflation in the developing country of Tunisia, by means of annual data base (1970-2008), univariate and multivariate tests of structural breaks, and cointegration analysis with multiple structural changes. Our empirical results indicate that by positively impacting the price level, oil price negatively impacts real output. The results also indicate that in Tunisia the monetary policy responds to a surge in the oil price in order to reduce or sustain any growth consequences. The ensuing higher inflation however prompts a subsequent tightening of monetary policy leading to a further decline in output. In addition, output does not revert quickly to its initial level after an oil price shock, but declines over an extended period.