Semantic extensions of spatial deictics and of verbs meaning ‘come’ and ‘go’ have aroused interest in the context of studies of grammaticalisation. Reflexes of the Proto Polynesian directional particles *mai ‘towards speaker’/venitive, *atu ‘away from speaker’/andative, *hake ‘upwards’ and *hifo ‘downwards’ show the development of psychological, expressive and temporal meanings from concrete (in this case spatial) meanings which has been seen as central to many cases of semantic change. This discussion of Tokelauan mai and atu is based on a quantitative analysis of a corpus of spoken Tokelauan. In most types of discourse, the expression of spatial deixis is by no means the most frequent use of the particles. Uses relating to communication, perception, emotion, point of view and speaker’s attitude predominate. Most interestingly, there is also evidence for the development of aspectual functions. I show that the venitive particle mai can function as a marker of continuative aspect and that this development arises from its temporal and evidential uses. The andative particle atu can indicate ingressive aspect, particularly in certain idiomatic collocations and in ‘begin’ constructions. These meanings lack spatial content, but the deictic element is always detectable, though at a more abstract level.