The article discusses multi-senses connectives and their annotation in text corpora.The author clarifies the concept, which is usually applied to three different phenomena: i) the uncertainty of annotators in choosing one of the meanings of a polysemic connector; ii) the possibility of establishing more than one relation, both explicit and implicit, between two fragments of text; iii) the "combination" of several meanings by a connective.The author then considers how these cases are annotated in the Penn Discourse Treebank and in the Supracorpora Database of Connectives, which use a multi-label annotation for discourse relations.The study also raises a number of theoretical questions: what information can we obtain from double labels, which relations are distributionally close, i.e. can be established in the same contexts, how to separate the contribution of the connective and of the context to the overall meaning of a sequence of sentences, how legitimate is it to talk about the combination of meanings by the connective, how to annotate the features of the context of the connectives so that this data can be used for Natural Language Processing?The solution to these questions is important for both theoretical cognitive and applied research (in particular, for machine learning and machine translation).