Summary: This article presents an empirical Bayes method for estimation of the transition probabilities of a generalized finite stationary Markov chain whose \(i\)th state is a multi-way contingency table. We use a log-linear model to describe the relationship between the factors in each state. The prior knowledge about the main effects and interactions will be described by a conjugate prior. Following the Bayesian paradigm, Bayes and empirical Bayes estimators relative to various loss functions are obtained. These procedures are illustrated by a real example. Finally, asymptotic normality of the empirical Bayes estimators are established.