The well-known CUSUM test for structural change is investigated whe n there are lagged dependent variables among the regressors in a linear model. The authors show that both a modified CUSUM test, suggested b y J. M. Dufour (1982), and the straightforward CUSUM test retain their asymptotic significance levels in dynamic models, and find that the power depends crucially on the angle between the mean regressor and the structural shift. Copyright 1988 by The Econometric Society.