Recent plebiscites in EU member states, in particular the Brexit vote, have given rise to the question of which forms of popular vote can be deemed adequate instruments for decision making in a demoicracy. In a first part, this paper elaborates the conceptual underpinnings and most basic institutional features of demoicracy, i.e. a union of citizens and peoples. Secondly, it explains the distinction between plebiscitary and direct democracy. After a critique of the arbitrary governmental practice of plebiscites in EU member states the author singles out the citizen-induced referendum right with binding votes on secondary legislation as the most legitimacy-enhancing for the EU for the time being. Given the structure of the EU as a demoicracy, the votes should be aggregated in accordance with the principle of double majority of citizens and peoples. The facultative referendum is weighed against the possibility of a veto right of a majority of national parliaments against secondary EU legislation. For the time being this latter option would be more in line with the traditions of representative democracy of EU member states but overburdens the parliaments and does not engage the citizens directly.