In recent years, there has been a tremendous continuing attention to-
wards the modelling and analysis of longitudinal data, although not much
attention is paid to the ordinal categorical data. The problem becomes
more complicated if the observation at every longitudinal time point is
multivariate, and every component of the response vector is ordinal categorical. We develop urn model-type joint probability models with different
correlation structures when the data are of a longitudinal bivariate ordinal
nature, and discuss the methods of their estimation. Some examples which
motivate us to model and analyse such kind of data are also discussed.