This paper reports on an extensive Monte Carlo study of seven residual-based tests of the hypothesis of no cointegration. Critical values and the power of the tests under the alternative of fractional cointegration are simulated and compared. It turns out that the Phillips-Perron t-test when applied to regression residuals is more powerful than Geweke-Porter-Hudak tests and the Augmented Dickey-Fuller test. Only the Modified Rescaled Range test is more powerful than the Phillips-Perron test in a few situations. Moreover in large samples, the power of the Phillips-Perron test increases if a time trend is included in the cointegrating regression.