This article analyzes the asymptotic behavior of the Dickey–Fuller unit root tests when the variable is generated under the breaking trend hypothesis. Our results show that the asymptotic behavior of these statistics allows for the rejection of the unit root hypothesis. This asymptotic finding contrasts with the results that can be found in the literature devoted to the analysis of the integration order of a variable in the presence of a structural break. However, some Monte Carlo exercises show that the argument of Perron (1989, Econometrica 57, 1361–1401) that the tests are biased in favor of nonrejection of the unit root hypothesis remains valid for sample sizes of practical interest.