This thesis derives new tests for structural stability in panels by extending the testing procedure proposed in Andrews (2003) originally developed for time series. The tests are robust to non-normal, heteroskedastic and autocorrelated errors, and importantly allows for the number of post-break observations to be small. The first test relies on parametric sub-sampling techniques to derive critical values. The second test accommodates the possiblity of a break affecting only some - and not all - individuals of the panel. This test statistic is shown to be asymptotically normal under mild assumptions, thanks to the cross-sectional dimension of panel data. This greatly facilitates the calculation of critical values with respect to the first test. Monte Carlo experiments show that the test has good size and power under a wide range of circumstances. Finally, the tests ares illustrated in practice in a study of the Euro's effect on trade