An idea going back to Plato's Meno is that knowledge is stable. Recently, a seemingly stronger and more exciting thesis has been advanced, namely that rational belief is stable. I sketch two stability theories of knowledge and rational belief, and present an example intended to show that knowledge need not be stable and rational belief need not be stable either. The second claim does not follow from the first, even if we take knowledge to be a special kind of rational belief. 'Stability' is an ambiguous term that has an internally conditional structure.