Generalized estimating equations (Liang, K. Y. and Zeger, S., 1986, Biometrika 73, 13-22) allow longitudinal or clustered data to be modeled with minimal assumptions about their dependence structures. Association structures for polytomous data have generally required the estimation of a large number of parameters. In many applications involving repeated categorical data, an ordinal structure is present. A range of association structures and computational methods for ordinal categorical data is described, based on the cumulative odds ratio, which allows much more parsimonious models. This permits the generalized estimating equation methodology to be used for smaller sets of ordinal data and with less effort expended on modeling associations. The method is illustrated on sets of ordinal data from medical studies.