The article focuses on a rather unexplored topic in NLP: parenthetical classification. Parentheticals are defined as any text sequence between parentheses. They have been approached from isolated perspectives, like translation pairs extraction, but a full account of their syntactic and semantic properties is lacking. This article proposes a new comprehensive scheme drawn from corpus-based linguistic studies on French news. This research is part of a project investigating the structural aspects of punctuation signs and their usefulness for Information Extraction. Parenthetical classification is approached as a relation extraction problem split into three correlated subtasks: syntactic and semantic classification and head recognition. Corpus-based studies singled out 11 syntactic and 18 semantic relation subtypes. The article addresses automatic classification, using a combination of CRF and SVM. This baseline system reports 0.674 (head recognition), 0.908 (syntax), 0.734 (semantics), and 0.518 (end-to-end) of F1.