What does the neologism demoicracy mean? If democracy is the “government” of the “people”, can there be a government of peoples? Within the last decade, the idea of demoicracy has developed considerable traction, especially within the political science literature on the European Union (EU). Yet what exactly is demoicracy conceptually supposed to mean in this context; and what models of demoicracy have developed to describe or prescribe the institutional structures of the European peoples governing together? This article offers a constitutional overview of the potentially democratic or demoicratic elements within the European Union and critically presents the three models of demoicracy that have developed in the contemporary literature on the European Union. It subsequently introduces a—new—fourth model called “republican federalism”, which sees the core feature of demoicracy in a majoritarian government among the peoples of Europe.