ABSTRACT Experiments where the response is a categorical variable are usually carried out in many fields such as agriculture. In addition, in some situations this response has three or more levels without an order between them characterizing a multinomial (nominal) response. Statistical models for scenarios where the observations of a nominal response can be considered independent have an extensive literature, such as the baseline-category logit models. However, situations where this assumption is violated (as in longitudinal studies) require specific models that take into consideration the dependence between observations. In this paper, a fairly new extension of the generalized estimating equations is applied to analyze an experiment carried out to investigate the type of vegetation observed in an elephant grass pasture, according to some management conditions over time. This extension uses local odds ratios to explain the dependence among the categories of the outcome over the repeated measurements. Two different structures were compared to describe this dependence, and the Wald test was used to select the significant variables. Further, we built confidence intervals for the predicted probabilities of occurrence of each category and assessed the results comparing observed/predicted values and using the diagnostic analysis. The results allowed to conclude that there are various significant effects for treatments and for time. The structure of local odds ratio also proved as a good way to describe the dependence between categorical responses over time.