In this paper, performance of the KPSS tests of Kwiatkowski et al. (Journal of Economics, 54, 159–78, 1992) and the generalized fluctuation tests (GFL) of Kuan and Hornik (Economic Reviews, 14, 135–61, 1995) and Kuan (Journal of Econometrics, 84, 75–91, 1998) are investigated for the null of stationarity against alternatives of unit root and structural changed individually. Simulation results show that both the KPSS and the GFL tests have similar size and power performance under different DGPs considered. The number of truncation lags used in estimating the long-run variance plays a crucial role in test performance. Under the null of stationarity, the GFL tests have less size distortion than the KPSS tests given the same number of truncation lags. On the other hand, the KPSS tests have better powers for detecting structural changes occurring at the beginning and the end of a sample. This finding suggests that a more robust inference for the null of stationarity can be obtained by combining both information from the KPSS and the GFL tests.