The notion of cognitive system is widely used in explanations in cognitive psychology and neuroscience. Traditional approaches define cognitive systems in an agent-relative way, that is, via top-down functional decomposition that assumes a cognitive agent as starting point. The extended cognition movement challenged that approach by questioning the primacy of the notion of cognitive agent. In response, [Adams, F., and K. Aizawa. 2001. The Bounds of Cognition. Oxford, UK: Wiley-Blackwell.] suggested that to have a clear understanding of what a cognitive (...) system is we may need to solve “the demarcation challenge”: the problem of identifying a reliable way to determine which mechanisms that are causally responsible for the production of a certain cognitive process constitute a cognitive system responsible for such process and which ones do not. Recently, [Rupert, R. 2009. Cognitive Systems and the Extended Mind. Oxford: Oxford University Press.] offered a solution based on the idea that the mechanisms that constitute a cognitive system are integrated in a particular sense. In this paper I critically review Rupert’s solution and argue against it. Additionally, I argue that a successful account of cognitive system must accommodate the fact that the neural mechanisms causally responsible for the production of a cognitive process are diachronically dynamic and yet functionally stable. At the end, I offer a suggestion as to how to accommodate this diachronic dynamicity without losing functional stability. I conclude by drawing some implications for the discussion on cognitive ontologies. (shrink)