A unified rank-based analysis is developed for two-way models with a grouping factor (unequal number of subjects per group) and a repeated measures factor based on a dispersion function assuming exchangeability of the errors within each subject. This analysis produces asymptotically distribution-free tests for general linear hypotheses, and multiple comparison procedures based on R-estimators. A Monte Carlo Study is conducted to investigate the small sample behavior of a rank test for testing the hypothesis of no interaction between the repeated measures and the grouping factors.