When resolving anaphora, the precise identification of the antecedent is sometimes difficult. In a first set of cases linked to abstract anaphora (“in that context”, “it happens”), the reason lies in the exact delimitation of the antecedent (previous verbal phrase? previous sentence? whole paragraph?). In a second set of cases, several concrete antecedents are possible and the hearer or reader cannot decide between them. Moreover, deciding is not mandatory to the comprehension of the utterance or discourse, and the antecedent can stay underspecified. This phenomenon can be called ‘underspecified anaphora', or anaphora with ‘fuzzy' or ‘vague' antecedent. We illustrate it with French data, and we propose a first classification of types of potential underspecified antecedent. We then deduce principles for their annotation.