In this paper we investigate principles of the representation of time and modality in terms of conceptual graphs. Based on the works of A. N. Prior, and C. S. Peirce, we suggest a formalism that takes into account the notion of ‘Now’, as a starting point for developing a formalism that can account for comprehension of texts involving temporal descriptions. We analyze the temporal structure of two short narratives and represent the structure using branching time models and Conceptual Graphs. We argue that the suggested CG representation is in fact more in accordance with Prior’s approach to time than Prior’s own idea of branching time.