From the outset of the European cross-border cooperation of the 1960s and 1970s, the Council of Europe and the European Union generated parallel routes in this matter. However, when the Council of Europe developed structures, the European Union implemented programmes. For a long time, the Euroregions appeared as the keystone and the masterpiece of the cross-border cooperation. More recently, the European Union has established a territorial formula which is named EGTC (European Grouping of Territorial Cooperation). The intertwining of the cross-border realizations between the Council of Europe and the European Union gives raise to specific spatial disfunctionings, namely confusion, redundancy, oversizing and entropy. The Pyrenees are an interesting case study to illustrate these evolutions. The paper concludes with some statements devoted to the limits and the weaknesses of the territorial models of cross-border cooperation.