A model is proposed for longitudinal ordinal data with nonrandom drop-out, which combines the multivariate Dale model for longitudinal ordinal data with a logistic regression model for drop-out. Since response and drop-out are modelled as conditionally independent given complete data, the resulting likelihood can be maximised relatively simply, using the EM algorithm, which with acceleration is acceptably fast and, with appropriate additions, can produce estimates of precision. The approach is illustrated with an example. Such modelling of nonrandom drop-out requires caution because the interpretation of the fitted models depends on assumptions that are unexaminable in a fundamental sense, and the conclusions cannot be regarded as necessarily robust. The main role of such modelling may be as a component of a sensitivity analysis.