Summary: The paper examines various tests for assessing whether a time series model requires a slope component. We first consider the simple \(t\)-test on the mean of first differences and show that it achieves high power against the alternative hypothesis of a stochastic nonstationary slope and also against a purely deterministic slope. The test may be modified, parametrically or nonparametrically, to deal with serial correlation. Using both local limiting power arguments and finite-sample Monte Carlo results, we compare the \(t\)-test with the nonparametric tests of \textit{T. J. Vogelsang} [Econometrica 66, No. 1, 123--148 (1998; Zbl 1055.62576)] and with a modified stationarity test. Overall the \(t\)-test seems a good choice, particularly if it is implemented by fitting a parametric model to the data. When standardized by the square root of the sample size, the simple \(t\)-statistic, with no correction for serial correlation, has a limiting distribution if the slope is stochastic. We investigate whether it is a viable test for the null hypothesis of a stochastic slope and conclude that its value may be limited by an inability to reject a small deterministic slope.