Cladism, today the dominant school of systematics in biology, includes a classification component-the view that classification ought to reflect phylogeny only, such that all and only taxa are monophyletic (i.e. consist of an ancestor and all its descendants)-and a metaphysical component- the view that all and only real groups or kinds of organisms are monophyletic. For the most part these are seen as amounting to much the same thing, but I argue they can and should be distinguished, in particular that cladists about classification need not accept the typically cladist view about real groups or kinds. Cladists about classification can and should adopt an explanatory criterion for the reality of groups or kinds, on which being monophyletic is neither necessary nor sufficient for being real or natural. Thus the line of reasoning that has rightly led to cladism becoming dominant within systematics, and the attractive line of reasoning in the philosophical literature that advocates a more liberal approach to natural kinds, are seen to be, contrary to appearances, compatible.