Risk measures incorporate a conservative or risk averse perspective in decisionmaking under uncertainty. Taking a variety of models for the potential outcomes into account, the distributionally robust decision is the most conservative decision among the decisions available. This paper investigates different versions of conditional risk measures and distributionally robust functionals in a multistage setting. The risk measures and distributionally robust functionals relate to adequate distances of the probability measures involved. It is demonstrated that distributionally robust decisions are continuous with respect to the related nested distance.