This paper deals with the semantics of French adverbials that can be used to localise the eventualities of a discourse (events and states) in space and/or in time. The discourses that are considered are narratives describing trajectories. We propose both a linguistic description and a formal representation in order to model the contribution of these adverbials to the spatio-temporal structure of a discourse. The descriptive part tries to classify temporal and spatial adverbials according to the different interpretations they can give rise (spatial, temporal and spatio-temporal). We show that several other factors also condition these possible interpretations (aspectuality, discourse context, etc.). The formalisation of adverbial semantics is done within Segmented Discourse Representation Theory.