The historical present (HP) is the use of the present tense to refer to past events, usually as part of a narrative. Most work on this topic has dealt with the functions of English HP, mainly within the context of tense switching in conversational narrative. Relatively little work focuses exclusively on HP in Spanish, and most of it deals with the function of HP in conversational narratives. There is a gap in the literature regarding the specific interaction between the semantics and pragmatics involved in the use of HP, especially with respect to the formal representation of this interaction. In order to fill this gap, this paper analyzes the use of HP within the Parallel Architecture framework (Jackendoff 2002) and examines the implications for the semantic/pragmatic structure. Language samples produced by native speakers of Spanish and data from a large Spanish corpus are used as part of the basis for analysis. The present study also explores how the use of the preterite and imperfect in narrative in the past parallels the use of the simple present and the present progressive in narrative within the present timeframe, and shows how this can also be fruitfully analyzed employing the Parallel Architecture. The result is an original model that extends the formal apparatus of the Parallel Architecture to an area where it has not been applied before, the interface between semantics and narrative structure.