Asymptotic tests for multivariate repeated measuresunder non-normality and unspecified dependence structure will be presented. Notwithstanding their broader scope of application, the method are particularly useful when a large number of repeated measurements are collected from each subject but the number of subjects per treatment group is limited. In some experimental situations, replicating the experiment large number of times could be expensive or infeasible. Although taking large number of repeated measurements could be relatively cheaper, due to within subject dependence the number of parameters involved could get large pretty quickly. Under mild conditions on the persistence of the dependence, asympototic multivarate tests are derived for three testing problems in repeated measures analysis. Simulation results provide evidence in favor of the accuracy of the approximations to the null distributions. Data on College Smoking will be used to illustrate the application results.