A Bayesian analysis of the parameter vector,W(Wj= number of elements in categoryj), of a multivariate hypergeometric distribution is considered. It is shown that if,a priori, Wis compound multinomial (CMtn), then,a posteriori, Wis a translated CMtn. Many properties of the CMtn distribution are derived. These include joint moments of all orders; a characterization in terms of independent compound Poisson variables, conditional distribution of one subvector given another, and joint distributions of disjoint and overlapping sums of the components.