Cross-over trials assign two or more treatments sequentially to the same subject; groups of subjects receive different treatment sequences. Both parametric and non-parametric methods of inference are available for cross-over trials with complete data. In this paper we develop methods for estimation and testing in cross-over trials with censored data, based partly on methods used for complete data. Our estimator is consistent for the true effects. Simulation results show that both of our proposed tests have approximately nominal size. We compare our procedures to a method for cross-over designs based on Cox regression proposed by France, Lewis and Kay. We demonstrate that our method of estimation is superior to the Cox-based method, which has considerable bias. Both of the tests presented here have more power than the Cox-based tests in all of the situations we investigated. The estimation and test procedures apply to other designs, such as parallel trials and repeated measures designs.