A competence model describes the abstract structure of a solution to some problem. or class of problems, facing the would-be intelligent system. Competence models can be quite derailed, specifying far more than merely the function to be computed. But for all that, they are pitched at some level of abstraction from the details of any particular algorithm or processing strategy which may be said to realize the competence. Indeed, it is the point and virtue of such models to specify some equivalence class of algorithms/processing strategies so that the common properties highlighted by the chosen class may feature in psychologically interesting accounts. A question arises concerning the type of relation a theorist might expect to hold between such a competence model and a psychologically real processing strategy. Classical work in cognitive science expects the actual processing to depend on explicit or tacit knowledge of the competence theory. Connectionist work, for reasons to be explained, represents a departure from this norm. But the precise way in which a connectionist approach may disturb the satisfying classical symmetry of competence and processing has yet to be properly specified. A standard ‘Newtonian’ connectionist account, due to Paul Smolensky, is discussed and contrasted with a somewhat different ‘rogue’ account. A standard connectionist understanding has it that a classical competence theory describes an idealized subset of a network's behaviour. But the network's behaviour is not to be explained by its embodying explicit or tacit knowledge of the information laid out in the competence theory. A rogue model, by contrast, posits either two systems, or two aspects of a single system, such that one system does indeed embody the knowledge laid out in the competence theory.