Abstract This paper discusses six different multivariate Zipf distributions by virtue of having Zipf marginals. Arnold and Laguna (International Studies in Economics, Monograph No. 10 (1977)) proposed four univariate Zipf distributions and Yeh (Technical Report, Department of Finance, National Taiwan University, 1998) studied several properties of these four generalized Zipf distributions. Their results can be extended to the m-variate ( m⩾3) discrete case and thus six different multivariate Zipf distributions are developed. The object of this paper is to study some distribution properties of these six multivariate Zipf distributions.