The article argues that the ‘crisis of Europe’, triggered by market and governance dysfunctionalities (summarized as the Euro crisis), represents a ‘critical moment’ in the evolution of a European society. This society so far does not offer much resistance to such critical moments which is due to its incapacity to form a demos capable of acting together. The existing European society – and this is the basic claim – is nothing but the sum of individuals living in ‘sub-European’ (mainly national) groups. The evolution triggered by this critical situation opens pathways to turn these peoples of Europe into something more than being a sum of peoples governed by supranational bureaucracies. To decipher such processes a model is presented using Hirschman’s idea of exit, voice and loyalty as mechanisms to generate social ties. Two points arise as crucial. The first is the observation that national societies which continue to provide foundational claims for people have turned into interest groups in the context of the European Union. This undermines not only the ontological nationalism still dominating the self-presentation of national societies in Europe, but it also offers evolutionary paths towards a society beyond national foundational claims in Europe. Yet it also provokes reactive processes such as the return to the self-contained nation (or even ethnic group). This is the core of the crisis of Europe. The systemic crises of the state and the market in Europe are speeding up an evolutionary process of people-making, the outcome of which could be either the regression to a people with foundational identities or to a people without foundational identities. The latter will be described as a postnational society, which would make an emerging European society the first really modern society.