SUMMARY A method is proposed for the construction of log-linear models for binary data from cross-over designs. The method parallels the construction, for such designs, of linear models for continuous data. Exact conditional and likelihood ratio tests can be constructed for comparisons of interest. It is shown how all the well known contingency table tests for analysing data from binary 2 x 2 cross-over designs can be derived in this way. Generalizations of the model to cater for the inclusion of baseline responses and covariates is seen to be straightforward.