Nonparametric tests are useful when underlying distribution of a population is unknown or sample size is quiet small to satisfy assumptions of a traditional F test. Nonparametric tests have a good usage in a sample which consists of observations from various populations, as well. Randomized block designs are purposive when experimental subjects vary in natural heterogeneity. Nonparametric tests which are suitable for two-way ANOVA designs where the blocks containing observations which follow an increasing or a decreasing trend are main focus of this study. A recently proposed nonparametric test which was developed as an alternative to Jonckheere test is modified for ordered alternative hypotheses in randomized complete block designs. This modification test and several nonparametric tests for detecting ordered alternative hypotheses in randomized complete block designs are compared empirically in a broad set of Monte Carlo simulations under different conditions. A numerical example is provided to illustrate test procedures. The modified test provides better performance than Jonckheere test in terms of type I error and power values whereas Hollander test provides slightly better power values among the other test statistics. In terms of type I error values, it can be stated that the most conservative test is Jonckheere test whereas, estimated type 1 error values of the other test statistics are usually closer to nominal level of alpha.