This contribution is devoted to the additive relation, at the core of the construction of all text types and genres, and the connectives that frame utterances linked by addition. Based on the hypothesis that additive connectives do not merely indicate the occurrence of this relation, but explicit and enrich it in a variety of ways, our primary goal is to describe the semantic contribution that these connectives make to the textual movements in which they enter. In the first part of the study, we present the main features of additive relations as well as an inventory of French adverbial additive connectives. In the second part, we describe in more details the class of serial adverbs (premièrement ‘firstly’, deuxièmement ‘secondly’ etc.), before turning to the additive connectives aussi and également (E. ‘also, too’). In the conclusions, we highlight the distinguishing properties of aussi and également used as connectives and point to issues to address in a follow-up study on additive connectives.