Abstract The panel variant of the KPSS tests developed by Hadri [Hadri, K., 2000, Testing for stationarity in heterogeneous panels. Econometrics Journal, 3, 148–161] for the null of stationarity suffers from size distortions in the presence of cross-section dependence. However, applying the bootstrap methodology, we find that these tests are approximately correctly sized. Keywords: Heterogeneous dynamic panelsMonte CarloBootstrapUnit root testscross-section dependence JEL Classification : C12C15C22C23 Acknowledgements The authors would like to thank participants at the 13th International Panel Data Conference held in Cambridge, United Kingdom, and an anonymous referee for useful comments and suggestions.