In many clinical trials, treatment efficacy is based upon response to a biological marker that is measured repeatedly during the course of follow-up. However, in some of these trials it is not clear, a priori, how treatment effects on the marker may manifest themselves or what kinds of effects are clinically meaningful and/or acceptable. It is, therefore, desirable to allow flexibility in design and monitoring process by not prespecifying a stopping rule or even the parameter on which inferences will be based. Using the more general results in Hu and Lagakos, this paper extends the idea of the repeated confidence intervals for a parameter (Jennison and Turnbull) to repeated confidence bands for the mean function of a repeated measure process. We illustrate the approach and some considerations in its application with the results of a recent AIDS clinical trial.