The use of analysis of covariance in conjunction with the multivariate approach to analyzing repeated measures designs is considered for designs involving between- and within-subject factors, one dependent variable, and one observation per subject on the covariate. Considerations fundamental to a knowledgeable application of ANCOVA in this situation are detailed including issues related to (1) the validity of the test of the main effect of the within-subject factor, (2) the desirability of an interaction between the within-subject factor and the premeasure score, and (3) the reliability of change scores. Tables providing upper bounds on the correlations of the covariate with change scores are provided. Numerical examples illustrating various analyses of repeated measures designs are also presented.