Methods for the analysis of within-subjects effects in multivariate groups by trials repeated measures designs are considered in the presence of heteroscedasticity of the group variance-covariance matrices and multivariate nonnormality. Under a doubly multivariate model approach to hypothesis testing, within-subjects main and interaction effect procedures are largely robust to the effects of heteroscedasticity when group sizes are equal, even when the data are nonnormal. However, these tests are highly sensitive to the effects of covariance heterogeneity when the design is unbalanced. An approximate degrees of freedom multivariate statistic given by Johansen (1980) is shown to be largely robust to the combined effects of these assumption violations for unbalanced designs, provided that the smallest of the group sizes is sufficiently larger than the product of the number of dependent variables times the number of repeated measurements minus one. (Contains 30 references and 7 tables.) (Author)