This chapter argues that the contemporary Union is segmented into four distinct forms of political authority. The first and second segments are constituted by the 'Community' and 'Union' methods. The third is Monetary Union. The fourth consists of an extra-territorial segment where Union policies and laws are systematically applied to non-Member States. The chapter examines by attempting to move up one level of analysis from differentiation in the Union's policies to differentiation in the Union's authority relations. It discusses why it is important to understand European integration as differentiated by authority relations. The chapter shows how authority relations vary across the foregoing segments. The chapter also examines the question of how differentiation and coherence in European integration relate to one another. One possible model for the external application of EU authority is through 'dynamic' arrangements under which non-member states in effect pre-commit to near-automatic convergence with Union policies and laws.