The contribution focuses on spoken language and, initially, reviews fundamental features of parenthesis. Secondly, it deals with the meanings and discourse functions of parenthetical sequences. Thirdly, it analyses parenthesis in the light of current characterisations of ellipsis. Most linguists agree that parenthesis is a communicative strategy whose motivation is connected with an additional piece of information. The introduction of an additional piece of information causes a disruption. By providing information in a position maximally convenient for the speaker but at the cost of processability for the hearer, parenthesis violates themaxim of manner and hence the cooperative principle.A lot of differentmeanings and discourse functions of parenthetical sequences have been hypothesised. The contribution proposes a distinction between, on the one hand, parentheticals expressing a proposition and a speech act that are separate and outside of the host's speech act and, on the other hand, parentheticals expressing a proposition that acts on the host's proposition and within the host's speech act. The analysis of parenthetical incompleteness phenomena shows that there are at least three types of parenthetical ellipsis, one of which challenges the common understanding of ellipsis.