This chapter will propose a model for the analysis of argumentative connectives (thus, therefore, but etc.) in political discourse. While argumentative connectives have traditionally been analysed as text cohesion devices (Halliday) or pragmatic markers (Schiffrin, Blakemore) in an Anglo context, we propose to analyse them as a closed set of expressions that code logical and argumentative relations between clauses, performing the double function of text cohesion and argument coding, inspired by linguistic polyphony (Ducrot, etc.). In this chapter we demonstrate the relevance of linguistic polyphony for the analysis of political discourse through a case study of the use of argumentative connectives in Nicolas Sarkozy’s speeches to the European Parliament. The study shows that argumentative connectives contribute to rhetorical effects such as naturalisation of discourse, the representation of shared European values as well as the involvement of the audience in a co-construction of argumentation.