Using a new iterative algorithm that tests for possible breaks in the coefficients and residual variances of recursively identified structural equations, we examine changes in the parameters of the oil market model of Kilian (2009). Our analysis reveals breaks in the coefficients of the oil production and price equations, together with volatility shifts in all equations. In particular, the medium term response of production to aggregate demand shocks increases after 1980 and the price response to supply shocks is more persistent from the mid-1990s. All variables evidence changes in the relative contributions of individual shocks to their forecast error variances.