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This paper develops a simple test for the null hypothesis of stationarity in heterogeneous panel data with cross-sectional dependence in the form of a common factor in the disturbance. We do not estimate the common factor but mop-up its effect by employing the same method as the one proposed in Pesaran (2007) in the unit root testing context. Our test is basically the same as the KPSS test with the regression augmented by cross-sectional average of the observations. We show that the limiting null distribution is the same as the test suggested by Hadri (2000), which is the Lagrange multiplier (LM) test without cross-sectional dependence. We also extend Hadri's test and develop the LM test allowing for cross-sectional dependence. We compare our augmented KPSS test with the extended LM test under the null of stationarity, under the local alternative and under the fixed alternative, and discuss the differences between these two tests. We use Monte Carlo simulations to examine the finite sample property of our tests.