Many methods are available to analyze incomplete longitudinal ordinal responses. In this paper a general transition model is proposed for longitudinal ordinal responses with random dropout. Maximum likelihood estimates are obtained for the transition probabilities when there are repeated observations. The likelihood function of the general model is partitioned to make possible the use of existing software to estimate model parameters. Some reduced forms of the model are also considered where for estimation of parameters in these models one has to use numerical optimization methods. The approach is applied to the well-known Fluvoxamine data. For these data, two important results, which have not been previously reported, are obtained: (1) some transition probabilities are estimated to be zero and (2) the model for current response, which conditions on previous response, removes the effects of some covariates that had previously been significant.