We consider inference in the class of conditionally Gaussian dynamic models for nonnormal multivariate time series. In such models, data are represented as drawn from nonnormal sampling distributions whose parameters are related both through time and hierarchically across several multivariate series. A key example—the main focus here—is time series of multinomial observations, a common occurrence in sociological and demographic studies involving categorical count data. However, we present this development in a more general setting, as the resulting methods apply beyond the multinomial context. We discuss inference in the proposed model class via a posterior simulation scheme based on appropriate modifications of existing Markov chain Monte Carlo algorithms for normal dynamic linear models and including Metropolis-Hastings components. We develop an analysis of time series of flows of students in the Italian secondary education system as an illustration of the models and methods. © 1997 Taylor & Francis Group, LLC.