We propose an approach to investigate the stationarity properties of individual units in a panel based on testing user-defined increasing proportions of hypothesized stationary units sequentially. Asymptotically valid critical values are obtained using the block bootstrap. This sequential approach has an advantage over multiple testing approaches, in particular if N is large and T is small, as it can exploit the cross-sectional dimension, which the multiple testing approaches cannot do effectively. A simulation study is conducted to analyze the relative performance of the approach in comparison with multiple testing approaches. The method is also illustrated by two empirical applications, in testing for unit roots in real exchange rates and log earnings data of households. The simulation study and applications demonstrate the usefulness of our method, in particular in panels with large N and small T.