According to the pragma-dialectical approach to argumentation, for analysing argumentative discourse, a normative reconstruction is required which encompasses four kinds of transformations. It is explained in this chapter how speech act conditions can play a part in carrying out such a reconstruction. It is argued that integrating Searlean insights concerning speech acts with Gricean insights concerning conversational maxims can provide us with the necessary tools. For this, the standard theory of speech acts has to be amended in several respects and the conversational maxims have to be translated into speech act conditions. Making use of the rules of communication thus arrived at, and starting from the distribution of speech acts in a critical discussion as specified in the pragma-dialectical model, it is then demonstrated how indirect speech acts are to be transformed when reconstructing argumentative discourse. Finally, contextual clues for reconstruction found in argumentative activity types are discussed.