This paper discusses asymptotic behavior of one- and two-parameter Poisson- Dirichlet models, that is, Ewens models and its two parameter extensions by Pitman, and show that their asymptotic behavior are very different. The paper shows asymptotic properties of a class of one- and twoparameter Poisson-Dirichlet distribution models are drastically different. Convergence behavior is expressed in terms of generalized Mittag-Leffler distributions in the statistics literature. The coefficients of variations of suitably normalized number of clusters and of clusters of specific sizes do not vanish in the two-parameter version, but they do in one-parameter Ewens models.