We address the issue of deixis-anaphora in sign language (SL) discourse, focusing on the role of eye-gaze. According to the Semiological Approach, SL structuring stems from a maximum exploitation of the visuo-gestural modality, which results in two modes of meaning production, depending on the signer's semiotic intent. Involving both nonmanual and manual parameters, the first mode, expressing the intent to say while showing, uses constructions based on structures, the termed "transfer structures." The second one, expressing the intent to say without showing, involves lexical, pointing and fingerspelling units. In order to situate our descriptive concepts with respect to those used by SL linguists who, like us, adopt a cognitive-functionalist perspective, we expose a specific theoretical foundation of our approach, the "enunciation theories." The concept of "enunciation" is decisive for understanding the role of eye-gaze, as being at the foundation of deixis and the key vector of referential creation and tracking in SL discourse. "Enunciation" entails the opposition between "Enunciation" and "Utterance" Domains. The first links, as co-enunciators, the signer/speaker and his/her addressee, establishing them by the very "act of enunciation" as 1st and 2nd person. The second is internal to the discourse produced. Grounding on corpora of narratives in several SLs (some with no historical link), we illustrate this crucial role of eye-gaze and the diversity of functions it fulfills. Our analyses, carried out in this perspective, attest to the multiple structural similarities between SLs, particularly with regard to transfer structures. This result strongly supports the typological hypothesis underlying our approach, namely, that these structures are common to all SLs. We thus show that an enunciative analysis, based on the key role of eye-gaze in these visual languages that are SLs, is able to give the simplest account of their own linguistic economy and, in particular, of deixis-anaphora in these languages.