This paper is about the kinds of theories of mind (ToM) that non-human primates can be supposed to possess. In relation to this topic I will consider three main issues: (1) What kinds of minds do non-human primates possess (e.g., do they ‘know’ or ‘believe’)? (2) Do non-human primates understand ‘overt’ mental states (e.g., attention) in others?; (3) Do non-human primates understand ‘covert’ mental states (e.g., knowledge) in others? The question ‘Do non-human primates have a theory of mind?’ seems to be addressed with the implicit assumption that either they do or they don't. And if they don't have a genuine theory of mind (whatever this is), then their apparently mentalistic feats must be reduced to uninteresting trial-and-error learnings. I will argue that, to understand the problem of non-human ToMs, it is necessary to consider an intermediate possibility: the practical understanding of overt mental states as expressed in intelligent social actions. In arguing this I will resort to the notion of implicit understanding and implicit representations, especially as they have been recently treated by Karmiloff-Smith (1992). I will concentrate my discussion on the great apes (chimpanzees, gorillas, and orang-utans), our closest evolutionary relatives, and will, after a brief discussion of the overt mental state of attention, speak of epistemic mental states like knowing or believing.