The theory of punctuated equilibrium, offers a potential explanation for the profound morphological changes that accompany isolation in caves. I consider three aspects of punctuation theory: the association of morphological change with speciation; periods of stasis; and the number of genes controlling a trait. If the evolution of cave organisms is associated with speciation, then speciose groups and cave species derived from other cave-limited species should show increased adaptation. Analysis of Kane and Barr’s data on the subspecies of Neaphaenops tellkampfi and Holsinger’s data on crangonyctid amphipods fails to provide any support for the hypothesis. If the evolution is characterized by long periods of stasis, then directional selection should be rare. An estimate of selection in a cave population of Gammarus minus indicates that directional selection is occurring. Third, if punctuation is important, characters associated with isolation in caves should be controlled by a single gene. Wilkens and others have found most characters in cave Astyanax to be controlled by between 3 and 7 genes. It is more useful to frame the question of evolutionary change accompanying cave invasion in terms of adaptive topographies. Several examples of its use are discussed, including assessing the role in selection in structural reduction, and the role of isolation in adaptation to cave life.