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We present the R package gMWT which is designed for the comparison of several treatments (or groups) for a large number of variables. The comparisons are made using certain probabilistic indices (PI). The PIs computed here tell how often pairs or triples of observations coming from different groups appear in a specific order of magnitude. Classical two and several sample rank test statistics such as the Mann-Whitney-Wilcoxon, Kruskal-Wallis, or Jonckheere-Terpstra test statistics are simple functions of these PI. Also new test statistics for directional alternatives are provided. The package gMWT can be used to calculate the variable-wise PI estimates, to illustrate their multivariate distribution and mutual dependence with joint scatterplot matrices, and to construct several classical and new rank tests based on the PIs. The aim of the paper is first to briefly explain the theory that is necessary to understand the behavior of the estimated PIs and the rank tests based on them. Second, the use of the package is described and illustrated with simulated and real data examples. It is stressed that the package provides a new flexible toolbox to analyze large gene or microRNA expression data sets, collected on microarrays or by other high-throughput technologies. The testing procedures can be used in an eQTL analysis, for example, as implemented in the package GeneticTools.