The comparison of two groups is a well-known problem. The usual statistical testing procedures are based on the equality of the distributions, both in the parametric case and the nonparametric case. The nonparametric Behrens-Fisher problem extends to the case of non-equality of underlying distributions. This talk examines this problem in the multidimensional case, specifically controlling the Type I error probability and increasing power for detecting the alternatives. Some Monte Carlo simulations are given to examine the statistical properties. Some examples in biomedical studies are given to illustrate the procedures.