In autonomous multi-agent systems, agents communicate with each other in order to cooperatively resolve problems and achieve joint goals. In advanced applications such as e-business, agents should be able to communicate not only by exchanging simple massages, but by engaging in complex conversations such as persuasions and negotiations. In this paper, we address the computational complexity problem of such conversations where agents are equipped with reasoning capabilities based upon argumentation. We argue that the computational efficiency of these conversations depends on the underlying logical language and on the type of reasoning mechanisms. In addition, we show how a trade-off between complexity andflexibility could be achieved. ©2008 IEEE.