We suggest a rescaled variance type of test for the null hypothesis of stationarity against deterministic and stochastic trends (unit roots). The deterministic trend can be represented as a general function in time (e.g., nonparametric, linear, or polynomial regression, abrupt changes in the mean). Under the null, the asymptotic distribution of the test is derived, and critical values are tabulated for a wide class of stationary processes with short, long, or negative dependence structure. A simulation study examines the performance of the test in terms of size and power. The empirical performance of the test is illustrated using the S P 500 data.The authors thank the editor, the referees, and Karim Abadir for helpful comments and Alfredas Ra kauskas for drawing our attention to the criterion of Cremers and Kadelka (1986). The first author s work was supported by the ESRC grants R000238212 and R000239538. The last two authors were supported by a cooperation agreement CNRS LITHUANIA (4714) and by a bilateral Lithuania-France research project Gilibert.