The purpose of this paper is to investigate the tests of Hansen (1991) to detect structural breaks in cointegrated relations using Monte Carlo methods. The evaluation takes place within the linear quadratic model. The evidence for a single regressor suggests that the test have proper size and that the power is good provided the cost of adjustment is low. In addition to the tests of Hansen, we consider the sensitivity of the augmented Dicky-Fuller (ADF) teest for cointegration in the presence of a structural break. Our Monte Carlo experiments show that the ADF test suffers a substantial loss of power (a failure to reject the null of no cointegration). As a practical example we consider the stability of the long-run coefficients in annual U.S. money demand.