This paper addresses the problem of speech act recognition in written asynchronous conversations (e.g., fora, emails). We propose a class of conditional structured models defined over arbitrary graph structures to capture the conversational dependencies between sentences. Our models use sentence representations encoded by a long short term memory (LSTM) recurrent neural model. Empirical evaluation shows the effectiveness of our approach over existing ones: (i) LSTMs provide better task-specific representations, and (ii) the global joint model improves over local models.