Step size in evolution is rapidly becoming a major subject of interest to biologists. Traditionally, small changes alone were seen as significant in evolution, and any large differences between an ancestor and its descendant could be explained entirely by the accumulation of many small steps. Whether the evolution of major adaptations is mainly a matter of amassing such small increments of change, or if a significant proportion occurs through the inclusion of one or more large steps, is vital to the understanding of how evolution works. This paper begins by examining four ''classic'' examples of animalsflatfishes, turtles, bolyerine snakes, and gastropod molluscs-each of which has seemed difficult to interpret as resulting from a continuous series of tiny increments. Recently, however, arguments have appeared to contradict those views, and to propose instead that each of these animal groups arose through continuous adaptive modifications. While some of these arguments are more plausible than others, the view of the present author is that in none of them is there convincing evidence to conclude that the groups arose solely through gradual changes. More specifically, there is no basis to reject an evolutionary origin of the major traits in each group that included at least one principal inovation, occurring in a large, discontinuous step, preceded and followed by relatively small, more gradual changes. The broader question of how discontinuous evolution may occur is addressed through several means. These include considerations of epigenetic (sensu Waddington) development, comparative embryology, population genetics, and other approaches. Overall the phenomenon of adaptive accommodation is seen as of major importance, and its implications for ameliorating possible deleterious attributes of novel phenotypes are discussed. In the course of these analyses the doctrine that all adaptive evolution is driven by external environmental change is reviewed. It is suggested that while small adaptive changes are often closely related to shifts in specific environmental facets, the modifications associated with more major adaptations may be less so.