This paper considers unit root tests based on robust estimators with a high breakdown point and high efficiency. The asymptotic distribution of these tests is derived. Critical values for the test are obtained via simulation. It is found that the size of the classical OLS based Dickey-Fuller test breaks down if the time series contains additive outliers For innovative outliers the size of the robust test is less stable, while its size-adjusted power properties are better. An example is provided by applying the robust tests to the extended Nelson-Plosser data. For four series the null hypothesis of nonstationarity is rejected.