This thesis investigates the phenomenon of persuasion defined as the main intended perlocutionary effect political discourse can have on its audience. The main hypothesis is that particular elements (linguistic or other) contribute to the relevance of messages, and that the very relevance of messages can contribute in its turn to their persuasive effect, i.e. to the fulfilment of the main intended perlocutionary effect. The corpus is made up 2004 American and Romanian presidential debates, since presidential campaigns are a medium full of persuasive elements. The first three chapters of the thesis elaborated the theoretical framework suitable to test my main hypothesis. Presidential debates are tokens of a particular discourse type - political speeches. Chapter I investigates some possible definitions of discourse to outline several common characteristics. From the presentation of van Dijk's approach to CDA, the author retained that politicians do use different linguistic elements to achieve their goals and that an analysis of discourse structures can reveal what means they are employing in order to keep the processing effort low. This was further expanded in Chapter 4. Chapter 2 examined the two main models of communication (the code model and the inferential model) to be able to present an overview of Clark's theory of communication seen as joint action, and of Grice's contributions to the development of pragmatics. Without completely denying the existence of some sort of coordination involved in human communication, the thesis follows Sperber and Wilson's view of an asymmetrical coordination: speakers are the ones who have to assume correctly what codes and contextual information their audience have accessible and might use in comprehension. In an attempt to analyse what may have contributed to increasing/decreasing the persuasiveness of the political debates seen as ostensive-inferential stimuli, the author adopted Sperber and Wilson's relevance theory approach to communication as my main working hypothesis. The purpose of my thesis was to establish a link between relevance and perlocutionary effects. Chapter 3 examines the latter in the context of previous research. To have a sound basis for claiming that persuasion is a perlocutionary effect, the author shows what candidates to the presidency attempt to do through their speeches and what they want to affect in their audience: the answer was provided by Zimbardo & Leippe's (1991) definition of persuasion as involving the fulfilment of six steps. Chapter 4 was entirely dedicated to the corpus analysis. To support the analysis in 4.3, the findings were measured against the 2004 US and Romanian presidential results and several questions from the 2004 US and Romanian exit polls. The brief comparison in 4.4 shows that they were correct and realistic, thus confirming that the main hypothesis of this thesis is indeed feasible. In Conclusions, my findings are summarised and possible future lines of research are proposed.