Scientific practice involves two kinds of induction. In one, generalizations are drawn about the states of a particular system of variables. In the other, generalizations are drawn across systems in a class. We can discern two questions of correctness about both kinds of induction: (P1) what distinguishes those systems and classes of system that are ‘projectible’ in Goodman’s (Fact, fiction and forecast, 1955) sense from those that are not, and (P2) what are the methods by which we are able to identify kinds that are likely to be projectible? In answer to the first question, numerous theories of ‘natural kinds’ have been advanced, but none has satisfactorily addressed both questions simultaneously. I propose a shift in perspective. Both essentialist and cluster property theories have traditionally characterized kinds directly in terms of the causally salient properties their members possess. Instead, we should focus on ‘dynamical symmetries’, transformations of a system to which the causal structure of that system is indifferent. I suggest that to be a member of natural kind it is necessary and sufficient to possess a particular collection of dynamical symmetries. I show that membership in such a kind is in turn necessary and sufficient for the presence of the sort of causal structure that accounts for success in both kinds of induction, thus demonstrating that (P1) has been answered satisfactorily. More dramatically, I demonstrate that this new theory of ‘dynamical kinds’ provides an answer to (P2) with methodological implications concerning the discovery of projectible kinds.