This paper proposes a formal framework which offers an external representation of conversations between conversational agents. Using this formalism allows us: (1) to represent the dynamics of conversations between agents; (2) to analyze conversations; (3) to help autonomous agents to take part in consistent conversations. The proposed formalism, called “commitment and argument network”, uses a combined approach based on commitments and arguments. Commitments are used to capture the social and the public aspect of conversations. Arguments on the other side are used to capture the reasoning aspect. We also propose a layered communication model in which the formalism and the approach take place.