We investigate a multi-stage version of the selection problem where the variation between solutions in consecutive stages is either penalized in the objective function or bounded by hard constraints. While the former problem turns out to be tractable, the complexity of the latter problem depends on the type of bounds imposed: When bounding the number of changes of a single item over all stages, the problem turns out to be strongly NP-hard in general, even if we may select only one item per stage and each item may change only twice over all stages. In contrast, when the number of changes at each stage is bounded over all items, the problem can be efficiently solved by reducing it to a minimum-cost flow problem.