The principal issue addressed in this article is whether the twin crises revolving around the Treaty establishing a Constitution for Europe and the EU budget for the years 2007-2013 can be explained by two contradictory trends: the striving for the political deepening of the process of European integration, as well as its reform, on the one hand; and the defence of the status quo and reluctance to change on the other? The essence of the reply offered in this article is: no; both developments are a consequence of one and the same process, which can be described as an attempt to build a Europe modelled on a state. However, in one instance this involves imparting a quasi-state shape to an institutional system, in which power would be concentrated in the hands of the most powerful entities, and in the other the attempt centres on a vision of a common market based on state intervention, i.e. on a budget of a redistributionary nature. This model is designated "the Duchy of Europe" in this article, and it is being defeated for political, economic and social reasons. This model is juxtaposed on the concept of a "Europe" System, that is, the building up of a European Union based on new principles, modelled on non-linear network systems which make it possible to react flexibly to change while preserving the stability of the whole system. The initiative for building a Europe based on new principles can be effectively advanced by the Central European countries, which are to a lesser extent "captives" of the current arrangements.