Publisher Summary This chapter focuses on nonparametric simultaneous inference for some multivariate analysis of variance (MANOVA) models and presents simultaneous inference procedures based on general rank order statistics and derived estimators. One of the basic reasons for advocating the use of rank statistics and estimates is their good robustness against outliers and gross-errors. For nonparametric procedures considered in the chapter, any specific form of the underlying distributions (only continuity or sometimes symmetry suffices) is not required, and hence they enjoy a broader scope of applicability. They are robust. But, to meet this scope in full, the exact percentile points of the null distributions of various nonparametric statistics on which simultaneous procedures rest should be computed. For general rank statistics, these distributions can be enumerated by reference to suitable permutational invariance structures. The distributions of various nonparametric statistics are usually dominated by their asymptotic forms so that the use of asymptotic percentile points results in conservatism and does not affect the validity of these procedures. On the other hand, it leads to some loss in efficiency (or power); this loss is usually very small when sample sizes are large.